Dead-end microfiltration as advanced treatment for wastewater

DESALINATION ELSEVIER

Desalination 127 (2000) 47-58 www.elsevier.com/locate/desal

Dead-end microfiltration as advanced treatment for wastewater J. Agustin Suarez, Jose M. Veza* Department of Process Engineering, University of Las Palmas de Gran Canaria, Campus Tafira Baja, E-35017 Las Palmas de Gran Canaria, Spain Fax +34 (928) 458975; email:[email protected] Received 23 February 1999; accepted 1 July 1999

Abstract

This paper assesses the results obtained from a microfiltration pilot plant operating with effluent water from an activated sludge reclamation plant as compared with those predicted by two models: the "resistances in series" and the "blocking laws" models. The microfiltration unit consisted of hollow-fibre membranes and it worked with direct flow. the characteristics of the feed water varied with time depending on the treatment plant operation and on the characteristics of raw feed water. Therefore, it was impossible to work with a desired composition and the unit worked with a real and variable feed water. Two sorts of experiments were conducted: a series in which flow rate was kept constant (ranging from 6-7 m3/h during 60 min), and a second block, also in 60-min cycles, where neither the flow nor the transmembrane pressure were controlled. Finally, the experimental data were in good agreement with the model. Keywords: Microfiltration; Wastewater; Dead-end

1. Introduction Membrane separation processes are increasingly used as an alternative to conventional industrial separation methods since they potentially offer the advantages of highly selective separation, separation with any auxiliary materials, ambient temperature operation, usually no phase change, continuous and

in small units, as well as relatively low capital and running costs. Microfiltration (MF) is a pressure-driven membrane separation process which can separate solutes and colloidal particles of sizes greater than 0. I #m using a pressure difference o f usually 10-200 kPa as the driving force. MF is used in a wide variety of industrial applications such as

automatic operation, economical operation also

biotechnology and wastewater treatment. The latter has gone earning importance in the last

*Corresponding author,

years due to two main reasons: on one hand, to

0011-9164/00/$- See front matter © 2000 Elsevier Science B.V. All rights reserved PII: S 0 0 1 1 - 9 1 6 4 ( 9 9 ) 0 0 1 9 !-5

48

J. Agustin Suarez, J.M. Veza/ Desalination 127 (2000) 47-58

the shortage of drinking and irrigation water in many regions of the plant, which is demanding the development o f new sources and reusing techniques; and in addition, the necessity of increasing or removing the polluting substances dumped in the environment. Benitez [1] used a MC unit inside a bioreactor to stabilize and dewater some industrial wastewater. The module type used was a hollow-fibre membrane with dead-end aerobic stabilization of organic wastes and the solid-liquid separation tanks for a unique biological reactor. Also, Shimizu et al. [2] used a cross-flow MF module with hollow-fibre membranes to treat some urban wastewater. The cross flow was obtained by air bubbles which rose tangentially to the membranes. The purpose of this paper is to analyze the behaviour of a dead-end MF pilot plant operating with secondary effluent and check it against the resistances in series and the blocking laws models,

Table 1 Raw feed characteristics Parameter

Range

Average

pH 7.5-8.2 Conductivity,#S/cm 2320-3490 Turbidity,NTU 7-49 Suspendedsolids, mg/L 13-96 Dissolvedsolids, mg/L 1340-2730 BODs,mg/L 13~80 COD, mg/L 68-214

7.8 2900 15 33 1640 32 118

COT soluble, mg/L Total coliforms

9-55 1.26-8.25 x

30 3.85×106

(cfu/100 mL) Fecal coliforms (cfu/100 mL)

10 6

15,000-864,000243,000

Source: DEREA [3].

2. Materials and methods

only five were used due to a breakdown of one o f them. Each one o f those modules contains about 18,000 polypropylene hollow fibres 310#m internal diameter and 170/~m thickness each, with a nominal 0.2/~pore size. The total filtration

All the experimental work was done on a MF unit (Memcor 6M10C) with hollow-fibre

area of the five modules was 75 m 2. The experimental set-up in shown in Fig. 1.

membranes, set up in the R&D centre DEREA in Gran Canaria (Spain). The feed water was filtered secondary effluent with no chlorination from a nearby wastewater treatment plant whose characteristics are shown in Table 1 [3]. This activated sludge plant can process about 7000 m3/d wastewater, The unit is a compact and modular apparatus and consists o f the membranes, a circulation pump, the associated valves, pipework, instrumentation and a control system. A programmable logic controller (PLC) controls the unit operation, and it also monitors various parameters such as pressure, flow, pH and conductivity. It also has a 4001 storage break tank and a clean-in-place (CIP) system, The unit has six filtration modules, although

2.1. Description o f the process

During MF, the feed water is fed to the break tank after passing through a 400/,zm sieve. Then it is pumped to the filtration modules. The water flows from the outside of the fibres to the inside of them where the filtered water is collected. The operational pressures is 260-280kPa, with a pressure drop across the membranes, called transmembrane pressure, of 20-120kPa. The equipment was designed to operate in the direct (dead-end) filtration mode during a period of time up to 60 min, depending on the characteristics of the effluent, followed by an automatic backwash cycle with air and raw water. The backwash consists of injection o f air at about

J. Agustin Suarez, J.M. Veza / Desalination 127 (2000) 47-58

49 PRODUCT

AIR

[ ....

T .......

.......

-¢'*

.......

-'1 :-r ........

:.~! i

......

~ ...........

2............

I ............

k ...........

2.~

1 '.-. . . . . . . .

F i g . 1. E x p e r i m e n t a l

v~

•

DRAIN

set-up.

6 bar pressure to the inside of the fibres to dislodge contaminants from the surface; afterwards, the contaminants are flushed away by a sweep of raw water flowing through the unit. During the experiments, operational pressure, transmembrane pressure and filtrate flow rate were recorded. The feed water was characterized by its turbidity using a Hatch turbidimeter, Because the feed came from a wastewater plant, it did not have any constant composition. This was depending on the characteristics of the raw feed to the treatment plant and on its own operational performance. That means that the feed water composition to the MF unit varied along the week and even during the day. Therefore, it was impossible to work with either a fixed composition or a desired composition for us. In other words, the unit was operated with actual feed water coming from a wastewater plant in operation. Two sorts of experiments were carried out: 1. Constant flow rate experiments. In a first series, flow was kept constant during cycles of

60min while transmembrane pressure and time data were recorded. The working flow rates were 6 and 7m3/h because these were next to the design flow rate, that is, 6.5 m3/h. The only way to keep a constant flow rate was by means of a manual valve at the product outlet. This could have produced a certain error to the recorded data. These experiments were grouped underthe heading of "constant flow rate". 2. Variableflow rate experiments. In a second experimental group, neither the flow nor the transmembrane pressure was controlled as occurs during regular plant operation. Transmembrane pressure, flow and time data were taken during cycles of60min. These experiments were under the caption of "variable flow rate".

3.

Theory

3.1. Resistances in series The resistances in series model has been used by several authors to analyze processes such as

J. Agustin Suarez, J.M. Veza/ Desalination 127 (2000) 47-58

50

ultrafiltration (UF) and MF. Thus, J6nsson [4] used it to study how the shear rate affects the filtrate flow in cross-flow UF. Jones et al. [5] developed a hydraulic model to cross-flow UF. Martsulevich [6] dealt also with a model based on resistances in series applied to cross-flow MF of a lubricant liquid. Benitez [1] worked with wastewater and used the model with dead-end MF. A mathematical development is presented here in two cases: constant and variable flow rates.

3.1.1. Constant flow rate Considering a membrane of MF as a porous filter medium, the Hagen-Poseuille equation [7] for laminar flow through the membrane pores applies:

Q

Cb Vp = Cp Vp +6 A Cbl

8~Z

rbl % -

Membrane thickness, porosity and pore radius are particular characteristics of the membrane and are collectively defined as the inherent membrane resistance [5], Rm:

8L EP2

(2)

whereas the membrane resistance will be increased by the deposit of particles on the membrane surface and inside the pores R, [1]. Then Eq. (1) becomes

AAP o - , (R,,, + Rs)

where % is the specific resistance of the boundary layer [1]; therefore, the flow rate can be expressed as A Ap

Q_~

(Cb-Cp)~o ]

ra +

A

(7)

Vp

Eq. (7) relates the flow rate, pressure drop across the membrane and the filtrate volume with time t. If Q remains constant, then

AP : gQ Rm+ t(7 (~ ~Wb--plO~°]aQ2 t A Az

(8)

Eq. (8) shows the pressure drop change during a filtration run with the elapsed time. Plotting AP vs. t during a filtration run with a constant flow rate should yield a straight line.

AP =AP 0

(:3)

+

--'(Cb-Cp)%gQ2t A2

3.1.2. Variable flow rate

with

R = 6rbl

(6)

Cbt

[R (l)

(5)

Substituting equations and considering Cbl as constant, we obtain

NT~r4Ap_eARZAP 8~L

em -

From a solids material balance where the amount of solids entering the membrane equals the amount leaving plus the amount deposited:

(4)

Since the usual operating regime of the plant is characterized by maintaining a variable flow and pressure drop, it is interesting to check that

J. Agustin Suarez, J.M. Veza / Desalination 127 (2000) 47-58

the experimental data fit Eq. (7) well. Consequently, it can be conveniently transformed into

A p - ~tRm d V A

(Cb-Cp)cXo~Vp dVp

dt +

A2

dt

(10)

Integrating Eq. (10) will assume a linear relationship AP vs. t. The assumption is confirmed during the tests, except for the initial 10min period,

AP o + A p t 2

V P

- --+['tRm (Cb-CP)t~°P V

A

2A 2

(11)

P

Taking this also into account that Q varies linearly with time during a filtration run, we obtain AP 0 +AP _ btRm + (Cb-C)%~t V

Qo +Q

A

2A 2

P

(12)

The left-hand-side term (AP 0 + AP)/(Qo + Q) can be plotted vs. Vp when the flow rate is variable, and the results should be a straight line.

3.2. Blocking laws The blocking laws were first introduced by Hermans and Bred6e [8] when studying the clarification of dilute suspensions (less than 100 ppm solids). The mechanisms underlying the blocking laws are purely mechanical, and the flux decline and transmembrane pressure increase are accounted for by the particles plugging the pores, In their original work, Hermans and Bred6e considered two extreme cases in the filter behaviour: (1) each particle entering the membrane completely plugs one pore on the surface (complete blocking law) and (2) small particles form an internal deposit on the walls of the pores, which causes a progressive restriction

51

of the free pore volume (standard blocking law). The intermediate blocking law was introduced empirically as a compromise between the complete and standard laws. Some years later, Grace [9] provided an extensive study of their application to various filter media, and he considered the constant flow rate ease. Hermia [10] sed the blocking laws in MF and developed a model himself. Since then several researchers have continued applying the blocking laws to MF. Bowen and Gan [11] microfiltered alcohol dehydrogenase from baker's yeast with polysulfone thin-film composite (TFC) membranes (Dow, Denmark), nominal 0.1 and 0.2#m pore size, and they quantified their results using the standard blocking law. Blanpain et al. [12] determined permeate flux and protein rejection for the MF of clarified beer using a Cyclopore membrane with a nominal 0.2/~m pore diameter. They also showed that the flux decay follows the standard blockinglaw. HlavacekandBouchet [13] carried out the MF of bovine serum albumin solutions at constant flow rate using track-etched Nucleopore membranes and microporous Millipore membranes, both with nominal 0.2gm pore size. They noticed that the intermediate blocking law best fit the pressure drop data. The theory is based on the following assumptions: (1) the membrane is considered as a bundle of parallel and straight pores with a radius r 0 and length L, (2) the flow regime is assumed to be laminar, and (3) each particle entering the membrane is captured. A mathematical development is presented here in two cases: when the flow rate is constant and when it is not.

3.2.1. Constant flow rate Complete blocking l a w -

According to the completely blocking law theory, at a constant flow rate [ 13], each particle coming into contact with the membrane perfectly plugs one pore. No

52

J. Agustin Suarez, J.M. Veza/ Desalination 127 (2000) 47-58

superimposition of particles is possible. The expression obtained for the transmembrane pressure is 1

eA

_

AP

Rml~Q

Rm~t Q

Ap-

exp eA

Rm~tQ

(13)

Initially, Vp= O, and at AP o, therefore

-

1 o Vp Ap o Rm~tQ

(14)

Standard blocking law - - According to the standard blocking law, the increase of the hydraulic resistance is the result of the constant deposition of particles inside the pores on their whole length. The analytical expression is now

l 1 _ 1 Nzc 2_ cVp X/r~-ff v/O ~ ~ L r° v/-Q ~/8r~U ~tL 3

(15)

Again, for Vp = 0 and constant flow rate, I

_

(17)

which can be once again transformed into

0V

Ap = Ap 0 exp

1 Ap

oV P eA

1

cV

A~ °

~8rcN~tL 3Q

oV

P eA

(18)

If the experimental data are suitably plotted, it is possible to determine if they fit any of the expressions (14), (16) or (18); consequently, if they are in agreement with the theory, the only variables are the transmembrane pressure Ap and the filtrate volume Vp. 3.2.2. Variable flow rate

Since the standard working regime of the plant is characterized by a flow rate and transmembrane pressure which change over time, the mathematical developed proposed by Hlavacek and Bouchet [13] at a constant flow rate was modifiedtosomeextenttobeabletovalidatethe experimental data against the blocking laws. Complete blocking l a w - - Modifying Eq. (13) and considering the initial conditions Vp= O, we obtain

(16)

Q _ Q0 AP

Intermediate blocking law - - the theoretical background of the intermediate blocking law was developed by Hermia [10]. Each particle is supposed to have the ability to be deposited on any part of the membrane surface. This means that, in this case, superimposition of particles is possible. It is also assumed that any particle depositiononaporecompletelyplugs it. Forthis case Hlavacek and Bouchet [13] obtained the following expression:

o - -

V

AP0 R m~t P

(19)

Standard blocking law - Similarly, modifying Eq. (15) and considering initial conditions yields

~p

i :

Q0 AP0

cV ~/87~N1aL3

(20)

J. Agustin Suarez, J. M Veza/ Desalination 12 7 (2000) 4 7-58 Intermediate blocking law - - The corresponding equation derived from (17) is

AP Q

AP0 oV - -exp ___e_; Q0

(21)

EA

According to Eqs. (19) and (2), both Q/Ap and (Q/AP) v2 plotted vs. Vp should yield straight lines. And Eq. (21) results in an exponential function when AP/Q is plotted vs. Vp, thus allowing us to validate the experimental data and determine if the blocking laws are in good agreement.

180

,,,

fit

53

linc /

----tit li~ b~,

,,o "'

R 2 = 0.9718

'* ,o

.

. o,j,s

,~"

~""

R2= 0.9879

,, 2,

,',

2',

,',

,,

t (min) 4. R e s u l t s a n d discussion

The results are validated against both proposed models: resistances in series and blocking laws.

Fig. 2. AP vs. t. Q = 7 m3/h.

0 at ~inc 2

4.1. Resistances in series 4.1.1. Constant f l o w rate

In order to see how the resistances in series model fits the experimental data, Ap was plotted vs. time to compare them with Eq. (9). Flows of 6 and 7 m3/h were used. Because of the characteristics of the plant, it was impossible to deal with a higher flow while keeping it constant. On the other hand, no difference was noticed at lower flows. The r u n s lasted no longer than 60min because of clogging due to the plant limitations. There were different clogging levels being observed yielding the same relative results. Only results for Q= 7 m3/h are shown here, and data for Q= 6 m3/h are quite similar. An example of these experiments is given in Fig. 2 for 7 m3/h. It is shown that the resistances in series model fits the experimental dat quite well (correlation coefficient R2=0.9461), although the agreement is slightly better if an initial transition period of time is considered.

....

. .....

fit line bis . . / . ~ , , , "

~ '

"

. J

~ '

+~ ~ R2 = 0.9866 c~ 4 ~ . . . ~" '~ ~ z ~"~''"-" R2 = 0.9918 A

II

I

I

I

I

I

,

2

,

,

,

,

Vp(m3)

Fig. 3. (AP0 + AP)/(Qo+ Q) vs. v~.

That is to say, if some initial data (about 6 min) are neglected, it is observed that the others agree with a straight line (R2=0.9731). The latter correction is denoted by "fit line bis" on Figs. 2-4.

54

J. Agustin Suarez, J.M. Veza / Desalination 127 (2000) 47-58 14

ntnmc

. . . . at I~e b~ ,,

. ~ 7.s _ . . ' 7 " R2 = 0.98

H e n c e , R t can be obtained from Eq. (3) for several time instants. Since Q and AP are available experimental data, the surface area of the membranes is A = 75 m 2 and the water viscosity at 20°C is ~t=0.001002 Pa's. Fig. 4 shows R, vs. time for the same experiment as Fig. 2. Thus a relationship expressing R, as a function of time is obtained, with a coefficient R 2 = 0.9875:

-"9"-

'° 'E '

-~. ¢~

Rt =

0.0035 t + 0.9151

(23)

4

'

,

R2 =

Again an initial period is noticed with different behaviour. Neglecting the first data (for about 6min), a straight line is obtained with a better correlation coefficient (R 2= 0.9924). In this case the line equation is

0.9924

, . . . . . . " . . . . . . . . . . . . . . .t.(m) .............

Fig. 4. R, vs. t.

R, = 0.0037t + 0.5435

4.1.2. Variable f l o w rate Plotting Ap and Q vs. time from a variable flow experiment (not shown) would render ahigh linearity, with a correlation coefficient R 2 = 0.9826 for Ap and R2=0.9777 for Q. For t=0, AP 0= 53,043 Pa and Q0 = 0.002 m3/s. In order to check the resistances in series model when both the flow rate and the transmembrane pressure are not constant, (AP 0 + AP)/(Qo+ Q) was plotted vs. Vp (Fig. 3), as compared to Eq. (12). Good agreement (R2=0.9866) was observed with the model. Again, if some initial transition period is considered, somewhat better agreement is noticed (R 2= 0.9918).

which would be valid for t ~ 6 min. In any event, the inherent resistance of the membrane is, according to the experimental data, Rm=2.2xl012 m -1. It must be taken into account that R,, is due not only to the membrane itself but also to the solids which were not able to be removed during the backwash. This means that R m is different from a filtrate cycle to the next one because of the irreversible deposit o f the particles over the membrane. This deposit is only removed when chemical cleaning of the membranes is carried out. Both Eqs. (23) and (24) show thatR t increases over time. This is due to the dead-end mode because every solid coming to the membrane settles over it. As a result, the deposit continuously

4.2. Rt variation with time

Furthermore, the total resistance variation was studied. This resistance is due to the membrane itself and to the particles deposition over the membrane surface and inside the pores. This resistance has been called R t , and it is defined as: R t -- T +R s

(22)

(24)

grows; on the contrary, there would be a difference in cross-flow mode. The latter was concluded by Jones et al. [5] after realizing that R t increases at the beginning until a limit value is reached, which remains constant. That is because from a certain moment, the shear rate is enough to avoid the growth of the deposited layer. As a result, the deposit and, therefore, R t stabilizes. However, this is different in dead-end MF.

J. Agustin Suarez, J.M. Veza / Desalination 127 (2000) 47-58

4.3. Blocking laws 4.3.1. Constantfiow rate In order to see whether the blocking laws fit the experimental data, two experiments were considered with flow rates of 6 and 7m3/h, respectively. The data for Q= 7 m3/h were plotted in three different ways. First, 1/AP was plotted vs. filtrate volume Vp (Fig. 5) to compare with Eq. (14), corresponding with the complete blocking law; second, 1/(AP) 1/2vs. Vp (Fig. 6) to compare with Eq. (16), corresponding with the standard blocking law; finally, Ap vs. Vp (Fig. 7) to compare with Eq. (18), corresponding with the intermediate blocking law. It is shown that the blocking law models fit the experimental data quite well. However, the agreement is much better when the standard and intermediate laws are considered, with a correlation coefficient R 2 higher than 0.98. As a result, it is possible to deduce that the hypotheses on which these models are based are rather an agreement with the experimental data; that is to say, the increase of the transmembrane pressure

55

when the flow rate is constant is mainly due to the partial pore plugging because of the deposition of particles with a smaller diameter than the pore one, inside them on their internal wails. Moreover, to a certain extent the transmembrane pressure diminution can be due to complete pore plugging because of particles with a higher or equal diameter than the pores.

*" ~

.

~t~

'"

~_,° ,° ~

~',,x ~" - V ~ ' '

°0.

i

' "

0.0111

• . 0.01i

lt~

~' Vp ( m 3 )

~

'

"

Fig. 6. Standard blocking law. Q = 7 m3/h.

*

0.014 IIO

o.ol2

~,*

• li

14e 0.01o

O.OM

~

Ioo

|o 0.0~ ~o

O.OQ4

u 1

o 2

Vp (m3)

~ II

Fig. 5. Complete blocking law. Q = 7 m3/h.

* 4

4t I

1

Vp (m3)

S

4

Fig. 7. Intermediate blocking law. Q = 7 m3/h.

56

J. Agustin Suarez, JM. Veza/ Desalination 127 (2000) 47-58 4. 3.2. Variable f l o w rate

~"

In order to check the blocking law models when both the flow rate and transmembrane pressure are not constant, the following graphic representations were made, corresponding to a variable flow rate experiment ( Q / A P ) v s . Vp (Fig. 8) to the standard blocking law, which is given by Eq. (20); and A P / Q vs. Vp (Fig. 9) to the intermediate blocking law, according to Eq. (21 ). Since the flow rate is variable, to estimate the filtrate volume Vp, Q is assumed to change linearly (see Fig. 10), and hence an average value is taken to calculate the filtrate volume Vp. Good agreement was observed with mainly the standard and intermediate blocking laws with a correlation coefficient higher than 0.96. A similar behaviour was found at a constant flow rate. We can conclude that the transmembrane pressure increase and the simultaneous flow rate decline, when the filtration is carried out without any control of these variables, is due to (1) the deposition of particles inside the pores on their internal walls, as the standard blocking law postulates; and (2) the deposition of particles over the membrane surface, as the intermediate blocking law says.

J

j

".

/

~. ~

~

v"~ ,o ~ . ~ 5 o

R2=0.9879

.~°" .

~

'

,

,

~

, 2

,

, 3 vp (m3)

, 4

, ,

,

Fig. 9. Intermediate blocking law. Variable Q. ..... ..... ~

~'

o

' ' "

.-.

" .~ ~ 000,,

oR2=0.9777 o .

.

00012 20.0

i..o ~ ,60 -

°°°'°

= °

,o'° ,o'00 ,/0o doo do. doo .'o .....

t(s)

Fig. 10. Qvs. t.

% 14.0

0.9634

"°

~.:~

5.Conclusions

'°° -o ,o 4.0

z.o

|

,

i

,

I

,

!

,

Vp (m3)

Fig. 8. Standard blocking law. Variable Q.

I

,

A dead-end MF system has been tested with water from a municipal wastewater treatment plant, and it has been concluded that the resistances in series model fits the case in study quite well, and even better if a first transition moment is considered. During this transition period, the particles could be settling inside the pores in a higher proportion and also over the

J. Agustin Suarez, J.M. Veza / Desalination 127 (2000) 47-58

57

membrane surface in a lower proportion. During this transition time, the characteristics of the deposit are changing, and consequently rbl (resistance per unit length of the boundary layer) varies from zero to a value which becomes constant. In other words, both Eq. (9) for constant flow rate experiments (Fig. 2) and Eq. (12) for the variable flow rate experiments (Fig. 3) are a good approximation to the experimental data after rbt has reached its definitive value. The same behaviour is observed with the variation of R, with time. The total resistance is composed of a fixed value that is Rm plus the

Q r

---

rbl

--

R,, R~

R,

----

Vp

--

c%

--

variable R.,.. Initially, both r~l and Vp are null; during the transient period, rb~ and lip increase their value; and after some time, rbl iS stabilized and Vp continues to increase linearly, which means a linear variation of R,. since that moment (Fig. 4).

6

--

AP o

---

Regarding the blocking law models, the

e

--

experimental data fit the equations used quite well, either for a constant or variable flow rates

Membrane porosity, m 2 pore/m 2 membrane

P

--

Fluid viscosity (Pa s)

and transmembrane pressure. In order to check the models with the variable flow rate data, some mathematical transformation were made in the equations from the literature that deal with constant flow rate.

Filtrate flow rate, m3/s Pore radius, m Resistance per unit length o f the boundary layer, m -2 Inherent membrane resistance, m -~ Additional resistance, m -1 Total resistance defined according to (28), m -1 Cumulative fiitratevolume, m 3

Greek Specific resistance of the boundary layer, m/kg Thickness of the boundary layer over the membrane, m Transmembrane pressure, Pa Clogging coefficient (blocked area per unit of filtrate volume), m -I

Subscripts 0

--

Initial time

Acknowledgements 6. Symbols A - - Membrane surface area, m 2 c - - Volume of solid particles retained per unit of filtrate volume Cb

--

Cp

--

Ch/

--

L

--

N

--

The authors wish to acknowledge the support of the DEREA Project (Demonstration in Water Reuse), and specially the assistance of its technical manager, M. del Pino.

Bulk solution solids concentration, kg/m 3 Product solids concentration, kg/m 3

References

Boundary layer solids concentration, kg/m 3 Pore length, m, or membrane thickness Total number of pores in the whole membrane

[1] J. Benitez,A. Rodriguezand R. Malaver,Wat. Res., 29 (1995) 2281. [2] Y. Shimizu,Y.-I. Okuno,K. Uryu, S. Ohtsubo and A. Watanabe, Wat. Res., 30 (1996) 2385. [3] Informesobre la o p e r a c i 6 n y o p t i m i z a c i 6 n de las plantas del Centro de Investigaci6n y Desarrollo

58

[4] [5] [6] [7]

J. Agustin Suarez, J.M. Veza / Desalination 127 (2000) 47-58

DEREA (Demostract6n en Reutilizaci6n de Aguas) [in Spanish), 1996. A.-S. JSnsson, J. Membr. Sci., 79 (1993) 93. K.L. Jones, E.S. odderstol, G.E. Wetterau and M.M. Clark, J. AWWA, 85 (1993) 87. N.A. Martsulevich, Russ. J. Appl. Chem., 66 (1993) 1908. E.F. Brater and H.W. King, Handbook of Hydraulics fortheSolutionsofHydraulicEngineeringProblems, 6th ed., McGraw-Hill, New York, 1976.

[8] P.H. Hermans and H.L. Bred6e, J. Soc. Chem. Ind., 55T (1936) 1. [9] H.P. Grace, AIChE, 2 (1956) 307. [10] J. hermia, Trans. Inst. Chem. Eng., 60 (1982) 183. [ll] W.R. Bowen and Q. Gan, J. Membr. Sci., 80 (1993) 165. [12] P. Blanpain, J. Hermia and M. LenoEl, J. Membr. Sci., 84 (1993) 37. [13] M. Hlavacek and F. Bouchet, J. Membr. Sci., 82 (1993) 285.