Predictive models and factors affecting natural organic matter (NOM) rejection and flux decline in ultrafiltration (UF) membranes

DESALINATION Desalination 142 (2002) 245-255

ELSEVIER

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Predictive models and factors affecting natural organic matter (NOM) rejection and flux decline in ultrafiltration (UF) membranes Jaeweon Cho a*, Gary Amy b, Yeomin Yoon b, Jinsik Sohn c "Department of Environmental Science and Engineering, K-JIST, Gwan~u 500-712, Korea Tel. +82 (62) 970-2443; Fax +82 (62) 970-2434; email: choj@l~ist.ac.kr bCivil and Environmental Engineering, University of Colorado, Boulder, CO 80309, USA CDivision of grater Supply and Drinking graterManagement, Ministry of Environment, Kwacheon, Korea Received 29 March 2001; accepted 15 October 2001

Abstract

Prediction equations for NOM rejection were formulated using parameters, including specific UV absorbance [SUVA = UV absorbance at 254 nm/dissolved organic matter (DOC)] and af/kratio [a ratio of water permeability (D to the mass transfer coefficient (k)], which have been found to influence aspects of NOM and operating conditions, respectively. Attempts were made to formulaterelationshipsbetween adsorption resistance (Ro)and interfacial membrane concentration (Cm),and specifically between the amount of NOM absorbed (mg C/cm2) and the Ro.Flux decline was also formulated in two ways: (1) by the (so-called) empirical flux-decline equation with three flux-decline coefficients, and (2) by the adsorption flux-decline model with two NOM adsorption terms between bulk, the NOM and the membrane surface and an existing NOM adsorption layer. Keywords:

Natural organic matter (NOM); Flux decline; Ultrafiltration; Adsorption resistance; Adsorption fluxdecline model

1. Introduction

The series resistance model based on Darcy's law has been widely used to describe and predict flux-decline trends for protein filtration using UF membranes [1-3]. Aimar et al. [1] developed a *Corresponding author.

relation between the adsorption resistance for the series resistance model and the bulk protein concentration, and Gekas et al. [2] used a relation (between the adsorption resistance and the bulk protein concentration) to solve the solute mass transfer equation numerically for the concentration polarization boundary layer.

0011-9164/02/$- See front matter © 2002 Elsevier Science B.V. All rights reserved PII: S 0 0 1 1 - 9 1 6 4 ( 0 2 ) 0 0 2 0 6 - 0

246

J. Cho et al./ Desalination 142 (2002) 245-255

In the area of natural organic matter (NOM) filtration using an ultrafiltration (UF) membrane, the series resistance model was also used to formulate flux-decline trends using empirical expressions of irreversible and concentration polarization resistances with fitting coefficients [4]. Kinetic equilibrium adsorption of UF membranes with humic/fulvic acids was studied to evaluate the adsorption isotherm, representing the relation between the amount of adsorbed NOM and the bulk NOM concentration [5]. It appears that the relation between adsorption resistance and bulk NOM concentration is needed to formulate flux decline (during NOM filtration) using the physical and chemical parameters derived from adsorption expressions, such as the Freundlich-type or the Langmuir-type equations. These physical and chemical parameters can be correlated with NOM properties. The interfacial NOM concentration (between the membrane surface and the NOM near the membrane surface) can be substituted for bulk NOM concentration because NOM adsorption occurs inside the concentration polarization layer, and the interfacial NOM concentration may be calculated using the bulk NOM concentration, permeate flux, and mass transfer coefficient. Along with the series resistances model, which uses adsorption expressions, a completely empirical model (equation) is necessary to describe flux decline using fitting coefficients, which can be estimated easily using statistical tools, and these coefficients can also be correlated with NOM properties.

2. Experimental materials and methods

2.1. Membrane testing unit and membranes evaluated A cross-flow membrane unit (MiniTan, Millipore) was used to accommodate 60 cm 2flatsheet membrane specimens. The unit was comprised of a variable speed gear-pump with a relief

value and a back-pressure controller to control the transmembrane pressure. The feed flow rate (mL/min) was controlled and adjusted using the pump speed and a back-pressure controller. Feed flow rate increased when the pump speed was increased or the back-pressure controller was opened. Cross-flow (tangential) velocity (cm/s) near the membrane surface was calculated by dividing the feed flow rate by effective inlet area [membrane width (9.7 cm) x spacer thickness (0.04 cm)] of the membrane unit. The corresponding Reynolds number was approximately 100. Membrane permeate flow (mL/min) was measured by weighing a permeate sample collected over a certain time, and converted into a permeate flux (cm/s) by the dividing flow by the membrane surface area. There is diffusional mass transfer back to the bulk solution near the membrane surface, which is caused by the cross-flow velocity profile formed in the thin boundary layer. This diffusion transport can be denoted as a mass transfer coefficient (k, era/s) and may be calculated using Eq. (1) for laminar flow in flat rectangular channels [6]. UD210.33 k= 1.62 d--~-)

(cm/s)

(1)

where U is the average velocity of feed fluid (cm/s), D is the diffusion coefficient (cm2/s), dh is the equivalent hydraulic diameter (cm), and L is the channel length (cm). The diffusion coefficient may be calculated from the StokesEinstein relationship. The ratio of permeate flux (f= permeate flow rate/membrane surface area) to mass transfer coefficient (k) is defined as a relative flux (f/k) [7,8]. When the relative flux is 1.0, it can be theoretically assumed that the permeate flux (through the membrane pores; cm/s) is the same as the mass transfer coefficient (away from the membrane surface; cm/s); thus there is no net

247

J. Cho et al. / Desalination 142 (2002) 245-255

driving force acting on the molecules. When the relative flux is greater than unity, the permeation drag is greater than the lift force; thus NOM may have more opportunity to be adsorbed onto the membrane surface and are less easily rejected by the membrane surface. Two different membranes, polyamide (PA) GM and sulfonated polyethersulfone (PES) NTR7410, were used for membrane filtration tests to provide the relation between flux decline and NOM rejection. The molecular weight cutoffs of the GM and NTR7410 membranes were 8,000 and 20,000 daltons, respectively. A clean membrane was soaked into Milli-Q water one day before the test, Milli-Q was filtered through the membrane until the pure water permeability (PWP) stabilized, then a NOM-source water was introduced to provide flux-decline and NOM rejection, which continued until the permeability reached a steady state. Milli-Q was replaced with NOM-source water to remove the concentrated polarization layer, and a cross-flow velocity higher than the operating level was applied for 10 min to remove any gel layer. Then, the fouled membrane was taken out of the unit and cleaned with a 0.1 N NaOH solution for one day to remove the adsorption layer. The subsequent flux-decline result was used to provide a fluxdecline percentage (final flux divided by NOM/ initial flux) and to calculate the following parameters; series-in-resistances model [hydraulic (Rm), concentration polarization (Re), gel layer (Rg), weak adsorption (Ra0, and strong adsorption

(Ra2) resistances]. DOC and UVA at 254 nm of the bulk and permeate NOM samples were monitored over time to calculate NOM rejection.

2.2. N O M - s o u r c e w a t e r s

Several different NOM-source waters were used for the flux-decline and NOM rejection tests, including baseflow Silver Lake surface water (SL-SW), runoff SL-SW, Horsetooth Reservoir surface water (HT-SW), Irvine Ranch groundwater (IR--GW), and Orange County groundwater (OC-GW) (see Table 1). Each water exhibited a different DOC, UVA, specific UVA (SUVA = UVA/DOC), and humic fraction content. SUVA is an index of relative aromaticity. The humic fraction is estimated from the mass balance between raw water and the effluent using XAD-8 resin, as the XAD-8 resin effluent corresponding to the non-humic fraction of NOM. Humic fraction contents and SUVA values were correlated to provide a correlation, Eq. (2); this relationship can be used to predict the humic fraction of an NOM relatively easily using UVA and DOC measurements, but XAD-8 fractionation should be conducted to determine the exact value of humic fraction.

Humic fraction = 0.006 + 0.154 (SUVA) (2) r 2= 86%

Table 1 NOM-source water characteristics Source

UVA (cm-t)

DOC (mg/L)

SUVA (m-~mg-~L)

Humic fraction (% DOC)

Baseflow SL-SW Runoff SL-SW HT-SW IR-GW OC-GW

0.048 0.172 0.092 0.480 0.383

2.00 3.88 3.12 9.80 7.08

2.4 4.5 3.0 4.9 5.4

43 57 44 80 90

248

J. Cho et al. / Desalination 142 (2002,) 245-255

2.3. Data analysis methods DOC and UVA rejection were correlated with two possible parameters (SU-VA and f/k) by correlation analysis, which demonstrated a relatively high correlation between NOM rejection and these parameters. Multiple linear regression was then used to formulate a NOM rejection model with the two independent parameters, SUVA andf/k. Multiple regression was tested at the 95% significance level (0.05 rejection region) and by analysis of variance (ANOVA). A coefficient of determination [r2 = regression sum of squares (SSR)/total sum of squares (SST)] was used to determine a contributing portion using a regression equation, with a r 2 value of 1.0 indicating that the regression equation completely matches the model data. Permeate flux was monitored over time to compare different membranes and identify influential factors, and the flux ratio (final flux by NOM/initial flux) value was modeled using various independent parameters, including thef/k ratio, humic DOC, and non-humic DOC. Multiple linear regression was used to correlate flux ratio withf/k, humic DOC, and non-humic DOC at the o~o/..~i~nificance level.

3. R e s u l t s a n d d i s c u s s i o n

3.1. N O M rejection equation NOM rejections by GM and NTR7410 membranes, based on DOC and UVA, are shown along with NOM-source water, SUVA, and f/k ratio in Tables 2 and 3, respectively. Correlation values between NOM characters (SUVA and M,) and NOM rejections (based on DOC and UVA) are shown in Tables 4 and 5. Correlation between NOM rejection and SUVA was very high (about 0.92 and 0.97 for DOC and UVA rejection, respectively, for both GM and NTR7410 membranes), indicating that hydrophobic acids can be rejected easily by negatively charged membranes.

MW was found to be somewhat related to NOM rejection, but not meaningfully with SUVA. Performing multiple linear regression of NOM rejections by GM and NTR7410 membranes for independent influential parameters, SUVA and f/k, providedNOM rejection models, as shown by Eqs. (3) and (4), respectively.

DOC rejection (RDoc)= 0.251 + 0.134 x (SUVA -0.073 x (f/k) for GM

(3a)

2.3 < SUVA < 5.7, l
.!

1 0.8 A .~0.6

l

;~ o.4 1 0.2-

Izl m e a s m ~ D O C rejection zx cak~leted D O C rejection

•

measmrAUVArejvellon •

I.,

0

I

,

I

i

2

,

_

cal~Im~IUVArejeztion

I

3 SUVA

, 4

I

,

I

5

Fig. 1. Measuredand predictedNOM rejections by GM membrane. 1

I

I

I

r~ measuredDOC rejection O.S

0.6

m m e a s u r e d U V A r e j e c t i o n _, A calculated DOC rejection

"

3-

a

t~

calculated U V A r e j e c t i o n

t~

m 0.4

O.2 .

0

.

.

.

.

.

i

t

1

2

ix,, t.. 3

i

i

4

5

6

SUVA

Fig. 2. Measured and predicted NOM rejections by NTR7410 membrane.

J. Cho et al. / Desalination 142 (2002) 245-255

249

Table 2 NOM rejection by GM membrane NOM-source water

SUVA

f/k

DOC rejection (%)

UVA rejection (%)

Baseflow SL-SW Runoff SL-SW HT-SW HT-SW IR-GW OC--GW OC-GW

2.4 4.5 3.1 3.1 4.9 5.4 5.4

2 2 1 2 2 1 2

38 60 62 59 84 88 84

63 85 77 66 94 95 92

Table 3 NOM rejection by NTR7410 membrane NOM-source water

SUVA

f/k

DOC rejection (%)

UVA rejection (%)

Baseflow SL-SW Runoff SL-SW HT-SW HT-SW HT-SW IR-GW OC--GW OC--GW OC--GW

2.4 4.5 3.1 3.1 3.1 4.9 5.4 5.4 5.4

9.9 9.9 1 2 9.9 2 1 2 9.9

12 31 34 26 9 64 81 74 65

11 47 46 41 11 76 92 87 77

Table 4 Correlation between NOM characters and NOM rejection for GM membrane

SUVA MW

MW

DOC rejection UVA rejection

0.85

0.91 0.60

0.97 0.89

SUVA MW

U V A rejection (RuvA) = 0.467 + 0.102 x ( S U V A ) - 0.041 x (f/k) for G M

(3b)

2.3 < S U V A < 5.7, l
2.3 < S U V A < 5.7, l < f / k < 10, ra = 85.7%

MW

DOC rejection UVA rejection

0.84

0.93 0.74

0.97 0.84

U V A rejection (RuvA) = - 0 . 3 2 3 + 0.226 x ( S U V A ) - 0.014 x (f/k) for N T R 7 4 1 0

(4b)

2.3 < S U V A < 5.7, 1< f/k < 10, r 2 = 88.6%

D O C rejection (RDoc) = - 0 . 3 6 9 + 0.204 x ( S U V A ) - 0.065 x (f/k) for N T R 7 4 1 0

Table 5 Correlation between NOM characters and NOM rejection for NTR7410 membrane

(4a)

Figs. 1 and 2 s h o w c o m p a r i s o n s b e t w e e n experimentally m e a s u r e d and calculated N O M rejections b y Eqs. (3) and (4). S U V A and thef/k ratio could affect N O M rejections in t e r m s o f

250

J. Cho et al. / Desalination 142 (2002) 245-255

DOC and UVA. As SUVA increases, NOM exhibits more aromaticity and a greater negative charge density due to the carboxylic and phenolic groups of hydrophobic acids. As the f/k ratio increases, permeate flux becomes larger than the diffusional mass transfer coefficient away from the membrane surface, resulting in decreased NOM rejection.

3.2. Adsorption model The adsorption resistance term of the resistances in-series model [Eq. (5)] was correlated with the interfacial membrane concentration of NOM (C,,) to formulate adsorption equations. The value of C,, was calculated using Eq. (6). Estimated parameters describing a Langmuir-type relationship [Eq. (7)] and a Freundlich-type relationship [Eq. (8)] are shown in Table 6, and the experimental and predicted data from the isotherm equations are compared in Fig. 3.

resistance, Rc is the concentration polarization resistance, Rg is the gel layer resistance, Ro: is weak adsorption resistance, and Ro2 is strong adsorption resistance. (6) where Cp and Ch are the NOM concentrations of permeate and bulk samples, respectively, J is the permeate flux (cm/s), and k is the mass transfer coefficient (cm/s). Ra

J=

(5)

m

aC m

(Langmuir- type form)

l + b C I'tl 7o

(7)

[] Experimental ~ by Freundlich-type equationby Langrauir-type equation

60

5o ,

Ap

-

40

•

~"

~30

d

20 10

where Jis flux through the membrane (cm/s), Ap is transmembrane pressure [g/(cmxs~)], ~ is the dynamic viscosity [g/(cm x s)], Rmis the hydraulic Table 6 Parameters of adsorption equations of GM and MTR7410 membranes

t

Langmuir-type relationship: a b Sum of squares

NTR7410

11.92 0.276 1255

0.903 -0.010 2081

D

20

I

I

30

I

*

I

40

t

50

c, (rag/L)

I 60

* 70

Fig. 3. Experimental and modeled data of adsorption resistance (Ro) vs. Cm.

0.4

-' mRhlO

',,

LinearfitforNTR7410 ~

~0'3"J GM

I

10

I

I

I

~

'

Llne~fitforGM /

I

1/

Corml~on c o e f f l d m t = 9 5 . 3 % ~ f /J''

0.2

I °-'o It-

Collation ¢oeffldenlt--flS.1%

-0,1

Freundlich-type relationship: p q Sum of squares

0

22.48 0.145 1369

1.39 1.00 2199

20

40

60 80 100 Ra(x I0"D11cm)

120

140

160

Fig. 4. Adsorbed NOM mass vs. adsorption resistance (R.).

251

J. Cho et al. / D e s a l i n a t i o n 142 (2002) 2 4 5 - 2 5 5 Ra =

P(Cm)q (Freundlich-type form)

(8)

where a, b, p, and q are coefficients of the adsorption isotherm equation. Cm was calculated using Eq. (6), derived from the film theory.

strate the relationship between the adsorbed NOM mass and the adsorption resistance values (see Fig. 4). 3.4. Empirical flux-decline equation

3.3. Relationship between adsorbed NOM mass and adsorption resistance Adsorbed NOM (mg C / c m 2 ) , desorbed by treating with the NaOH cleaning solution, was plotted against adsorption resistance to demon-

Flux-decline values were compared with experimental and predicted data, calculated using Eq. (9) (see Figs. 5-8). Three flux-decline coefficients (k0, kl, and d) for GM and NTR7410 membranes with different NOM-source waters

e~ . a. ............

0.8

. .~ . . . . . . . . . . . . . . . . . . . ~ n ~n

Ifi]~/

0.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

O

~0.6 rr

i

rr

0.4

o.4 0.2

0.2

,., Ev4~mmtafl~rntlo z, Rradietedfl~raio m ExperlmmMfluKratlo .. R'edlctedfluxreiio i

I

i

2O

I

i

I

40 Time (h)

0

60

10

I

i

i

I

20

30

8O

Fig. 5. Experimental and predicted flux ratios o f GM membrane with H T - S W by empirical flux decline equation at f / k = 2.

I

i

40

i

I

i

50

I

i

60

70

Time (h)

Fig. 6. Experimental and predicted flux ratios o f the NTR7410 membrane with H T - S W by simple fluxdecline coefficients equation at f / k = 2.

1 0.8

I

i

i

1~ J~° 0.8

..................... 0 ~ ..~.. [].....

D

~'~ a

~-- . . . . . . . . . . . . . .

~--- ~ . . ~-- ~ . . . ~ - -

06-t- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

~0.6

!.

.j

0.4-

0.4 U,

0.2

0.2

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

t~ Experimentalfluxratio ~x Predictedfluxratio ,

I I0

i

I 20

t

I 30

,

I

40

;

I 50

i

I 60

t= Experimentalflux ratio ~x Predictedflux ratio ;

0 70

Time 0a) Fig. 7. Experimental and predicted flux ratios of GM membrane with O C - G W by simple flux-decline coefficients equation at f / k = 2.

i 0

I 20

i

I t 40 Time 0a)

I 60

t 80

Fig. 8. Experimental and predicted flux ratios o f NTR7410 membrane with O C - G W by simple fluxdecline coefficients equation at f / k = 2.

252

J. Cho et al. / Desalination 142 (2002) 245-255

Table 7 Flux-decline coefficients (k0, kl, d) comparison Membrane/coefficients

HT-SW

OC--GW

f/k=l

f/k=2

0.1017 0.0159 0.0000

0.1129 0.0750 0.0005

0.1152 0.0263 0.0000

0.1447 1.1775 0.0032

f/k=lO

f/k=l

f/k = 2

0.1011 17.99 0.0000

0.0956 0.2718 0.0025

0.1086 0.4446 0.0000

0.1064 4.9005 0.0034

f/k = lO

GM: kl d NTR7410: kl d

1.0756 0.3451 0.0041

1.6992 0.3517 0.0272

Table 8 Flux-decline coefficients (ko, kl, d) and final flux-decline ratio (J,/do) for GM membrane atf/k of 2.0 NOM-source

SUVA (mqmg- t L)

J~/'fo

ko

kI

d

Hydrophilic NOM of runoff SL-SW HT-SW Runoff SL-SW IR--GW OC--GW

2.3 2.9 4.4 4.9 5.7

0.853 0.874 0.759 0.828 0.794

0.084 0.1129 0.1564 0.1536 0.0956

11.78 0.075 25.07 4.699 0.2718

0.0014 0.0005 0.0026 0.0011 0.0025

Table 9 Flux-decline coefficients (ko, k,, d) and final flux-decline ratio (J~/Jo) for a NTR7410 membrane at anf/k of 10.0 NOM-source

SUVA (m- lmg- l L)

JJJo

ko

kI

d

Hydrophilic NOM of runoff SL-SW HT-SW Runoff SL-SW IR-GW OC-GW

2.3 2.9 4.4 4.9 5.7

0.633 0.44 0.397 0.5 0.233

0.233 1.076 1.102 0.3022 1.699

4.597 0.3451 0.4369 6.509 0.3517

0.0054 0.0041 0.0073 0.0105 0.0272

were calculated using a nonlinear regression (see Tables 7 through 9). Correlation o f the fluxdecline coefficients with SUVA and the final flux-decline ratio (Jt/Jo) are described in Tables 10 and 11.

"It = J0

1 / 1 + k 0 / 1 - e - k i t ] + dt

(9)

where k0 ( d i m e n s i o n l e s s ) r e p r e s e n t s the total

J. Cho et al. / Desalination 142 (2002) 245-255 Table 10 Correlation o f flux-decline coefficients (/co, k,, d) with feed water S U V A and final flux-decline ratio for a G M membrane with different N O M - s o u r c e waters

Final k0 kl d

J,/Jo

SUVA

Final J,/Jo

- 0.68 0.39 -0.12 0.59

-0.47 -0.61 - 0.92

3.5. Adsorptionflux-decline model As the concentration polarization resistance is small and negligible for UF membranes compared to the gel layer and adsorption terms in the series resistances model, a flux decline model can be formulated as shown by Eq. (10): AP-A~ St = ~ ~l{m +nad, l + nad,2)

(10)

where Ap is the applied transmembrane pressure (g/cm-s2), A~ is the osmotic pressure difference, Rm is the hydraulic resistance of the membrane (cm-~), Rod: is the combined term for the gel layer and the adsorption (between the membrane surface and NOM) resistances (cm- 1), and Rod.2is the gel layer or adsorption resistance derived from the interaction between an existing NOM gel (adsorption) layer and NOM in the bulk solution. The Rad,1 t e r m can be formulated as shown by Eq. (11) [2]. Rad,1 = Rae[1-exp(-P'Cm(t)q't)]

Table 11 Correlation of flux-decline coefficients (/Co,kl, d) with feed water SUVA and final flux-decline ratio for NTR7410 membranewith differentNOM-sourcewaters

Final ko kI d

flux-decline potential for a given membrane with a certain type of NOM, k~ (time -1) is the rate constant, which represents how quickly flux decline occurs, and d (time- 1) represents the fluxdecline kinetics.

(11)

253

J,/Jo

J,/Jo

SUVA

Final

- 0.78 0.539 -0.12 0.80

-0.94 0.69 - 0.78

where Rae is an equilibrium term of the Rod, p and q are parameters, and C,,(t) is the interfacial NOM concentration (mg/L) between the membrane surface and the boundary layer. The interfacial NOM concentration can be expressed as follows [see Eq. (12)]:

Cm(t)= Cb +(Cmax-Cb)e-k2t

(12)

where Cb is the bulk NOM concentration, Cm~xis the maximum value of the Cm(t),k2 is the kinetic parameter (time-1). The coefficient k2 should be related to the boundary layer mass transfer, and Cm~xshould be related to thef/k ratio. Considering adsorption between the adsorbed NOM layer and NOM in the bulk solution leads to a new adsorption resistance (Rad.2)expression [Eqs. (13) and (14)]: dRad'2 - k a C mRad,2

dt

(13)

where ka is an adsorption parameter.

Rad,2=Rae(ek°C*t-1)

(14)

Combining Eqs. (10), (11), (12), and (14) leads to the adsorption flux-decline model [Eq. (15)]:

d. Cho et al. / Desalination 142 (2002) 245-255

254

0.01

0.01 I

• 12 expetimemtal(f/k=l) ~, experimental(f/k=2) ~- - medeled(ffk=l) ~modeled(ff1¢=2) 0 exl~timental (ffk=lO)

0.008 -

....

m

.

.

.

.

.

.

.

.

.

.

.

.

.

.

~

~

i 0.004-

o ¢xpc~-imnat~(f&=lo) .........

0.004

.=.,,

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

-.

, 0

I

,

i

20

.................

~ 0.002

......................................

0

A experime~tal(Dk=2) ~ modeled (f/k-'=#2)

.

o.oo6

o. 0.002

12 experimemal(fTk=l)

0.008 - ~ - - ~ modeled (f/k-l)

i

l

40

O| ~

,

.

.

.

.

i

0

80

60

.

~,

20

.

~

i

I

i

40

I

D

,

60

80

T~c (h)

Time (h)

Fig. 9. Experimental and modeled (from the adsorption flux-decline model) data of NTR7410 membrane with HT-SW.

Fig. 10. Experimental and modeled (from the adsorption flux-decline model) data of NTR7410 membrane with OC-GW.

Table 12 Estimated equilibrium resistances and parameters of the adsorption flux-decline model with NTR7410 and HT-SW

f/k

Rao( x l 0 9 cm -I)

p

q

k2

ka

1 2 10

2.40 12.7 53.0

0.180 0.730 0.888

0.109 0.251 -0.734

0.0747 3.13 0.00788

0.00401 0.00388 0.00101

Table 13 Estimated equilibrium resistances and parameters of the adsorption flux-decline model with NTR7410 and OC-GW

f/k

Ra,(xl09cm-l)

p

q

k2

ka

1 2 10

1.97 9.82 102.3

0.157 0.984 0.234

0.170 0.623 0.111

4.04 0.0419 0.0905

0.00171 0.00210 0.00320

AP-A~

I~{Rm+RaeI-exp(-PCqt)+exp(kaCmt)]}

(15) Through this equation along with flux decline experiments, equilibrium adsorption resistance (Rot) and adsorption parameters (p and q) can be estimated without separate NOM adsorption tests. These estimated values can then be correlated with NOM properties.

The adsorption flux-decline model [Eq. (15)] was used to compare experimental flux decline with modeled flux decline (see Figs. 9 and 10). The estimated values of Roe,p, q, k2, and k~ are as shown in Tables 12 and 13.

4. C o n c l u s i o n s

Prediction equations for NOM rejection (DOC and UVA) can be developed in terms of the parameters SUVA and/or humic content, and the

J. Cho et al. / Desalination 142 (2002) 245-255 f / k ratio. Correlation between NOM rejection

(DOC and UVA) and SUVA is higher than that between NOM rejection and MW (NOM size), suggesting that electrostatic repulsion (from N O M acids with high SUVA) is more important than size exclusion (from NOM size) for NOM rejection. Langmuirian and Freundlichian equations can be used to correlate adsorption resistance with membrane concentrations of NOM, and in the present study, adsorbed NOM was shown to be related to adsorption resistance. The simple flux-decline coefficients equation and resistances model with hydraulic and adsorption resistances can be used to simulate flux decline. Flux-decline coefficients d and k0 were verified to be coefficients indicating quantitatively the total capacity of flux decline by correlation analysis results, and the coefficient k~ was found to represent a kinetic flux-decline trend. SUVA was related to total flux decline for a hydrophobic NOM-source water but not for a hydrophilic NOM-source water. Flux decline was also formulated by the adsorption flux-decline model with two NOM adsorption terms between the bulk NOM and the membrane surface, and the bulk N O M and an existing NOM adsorption layer.

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Acknowledgements This work was mainly supported by the A W W A Research Foundation (Project Manager: Traci Case), and also supported in part by the Korea Science and Engineering Foundation (KOSEF) through the Advanced Environmental Monitoring Research Center (ADEMRC) at K-JIST.

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