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E L S E V I E R Desalination 129 (2000) 23-33

DESALINATION

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Identification of diffusion modes of solutes in spiral-wound reverse osmosis membranes by interpreting tracing experiments

by a plug flow model

E. Roth*, B. Fabre, A. Accary Laboratoire Gestion des Risques et Environnement, UniversitO de Haute Alsace,

25 rue de Chemnitz, F-68200 Mulhouse, France Tel. +33 (3) 89 32 76 73; Fax +33 (3) 89 32 76 61; email: [email protected]

Received 6 December 1999; accepted 8 February 2000

Abstract

When you measure the rejection of a solute for a membrane, it only gives a global appreciation of the membrane capacity to reject this solute. This work analyzes the stimulus response experiments of different tracers in order to show their behaviour in composite polyamide reverse osmosis membranes. One new and three worn-out membranes have been tested to study the modification of solute transport in the membranes with wear. A dispersed plug flow model was used to identify the permeation modes of the solutes in the device. The distributions registered in the rejection side are unimodal and the residence time as well as the variance of the distributions obtained with the new membrane are smaller. The distributions obtained in the permeate of the new membrane are unimodal for the stimulus response experiments obtained with tracers like sodium chloride and hydrochloric acid. The stimulus experiment shows two maxima for sodium hydroxide. The presence of a second maximum for the NaOH tracing could be explained by the presence of a classical diffusion mode of NaOH in the polymer by "jump" added with acid-base reactions. In cases of worn-out membranes several maxima appear characteristic of permeation modes. The best model to represent the permeation of the solute is the dispersed plug flow model characterized by the Peclet number Pe and the tracer space time z in the device. Whatever the tracer, we can note the presence of three modes. The fourth, which is due to acid-base reactions, is present only in the NaOH tracings. The first mode is a remnant of the permeation that occurs in the new membrane. Modes 2 and 3 indicate the salt leakage. These new modes are to be linked with the decreasing of the density of worn-out membranes. Consequently, the rejection capacity of the membranes decreases.

Keywords: Dispersed plug flow model; Tracers; Reverse osmosis; Stimulus experiments

*Corresponding author.

0011-9164/00/$- See front matter © 2000 Elsevier Science B.V. All rights reserved

PII: S0011 - 9 1 6 4 ( 0 0 ) 0 0 0 4 8 - 5

24 E. Roth et aL / Desalination 129 (2000) 23-33

1. Introduction

Reverse osmosis (RO) is considered the best filtration method for obtaining ultrapure water. It is used to produce water for the semiconductor industry as well as to prepare dialyzing liquid [1 ]. These applications need very pure water in order to guarantee both the quality of the electronic device and the health of the patients. Membranes are elaborated in material having high water diffusion coefficients and low ones for solutes [2]. Measuring the rejection of a membrane for a chosen solute only gives a global appreciation of the membrane capacity to reject this solute [3]. We propose here to analyze the stimulus response experiments of different solutes in order to show the differences in their behaviour in a membrane. We have tested four FILMTEC FT30-4040 RO membranes (one new membrane FTN and three used membranes: FT1, FT2 and FT3).

Previous works have already described the study of a membrane with the stimulus response experiment techniques pointing out the presence of solute excursions from the feed channel to the membrane [4] and the easy characterization of the state of wear out of the membranes with the sodium chloride experiments [5]. In this work we compare the response of the membrane to three different components - - NaCI, HCI and NaOH solutions - - and try to link the physico-chemical properties of the membrane (density, intensity of ATR bands, rejection) with the characteristics of the stimulus response experiments.

By interpreting stimulus response experiments, we have found that a dispersed plug flow model describes the permeation of solutes across the membrane very well and explains the changes occurring with the wear out of the membrane.

2. Theory

2.1. Residence time distribution (RTD)

The concept of RTD was introduced in 1953 by Dankwerts [6] with the aim of studying the

hydrodynamics of a process by tracing. A real tracer is nonreactive with the system; it also represents the hydrodynamic of the studied system. This technique reveals the system dysfunctions like dead volumes, by-passes and recyclings which can be tracked by simple observation of its shape [7]. When the tracer reacts with the system, it means that there is a contact time distribution between the tracer and the system [8,9]. In the present case, the solutes injected into the membrane during the stimulus response interacts with it due to the rejection properties of the membrane.

The stimulus response experiment distributions E(t) recorded in the rejection side as well as in the permeate side are characterized by the mean residence time 7 of the tracer in the system and its variance 02 , which represents the square of the spread of the distribution. For continuous (resp. discrete measurements) they are defined as [7]

t= f t'E(t)'dt (resp. t= r t,'E,'At) (l) o

02 = f(t-7)2.E(t),dt o

[resp. a 2 = r t 2 . E , . k t - ( t - ) 2]

(2)

where (t,)i~ l are the equispaced measurement times and At is the measurement step.

2.2. Modelling stimulus response experiments

Fitting the distribution by a mathematical function does not give any information about the studied system. The approach developed to model the stimulus response experiments consists in modelling the distributions by assembling elementary cells with well-known stimulus

E. Roth et al. / Desalination 129 (2000) 23-33 25

responses [7]: ideal plug flow cell, dispersed plug flow cell, perfect mixing cell, by-pass, series of perfect mixing cells.

Later in this work, the dispersed plug flow model Ep(t) will be used. Its stimulus response is as follows:

,( ,t>21 E ( t ) = - ~ ~ .exp 4.r ; . t ] (3)

where Pe is the Peclet number, z the space time spent of the tracer.

3. Experimental

3.1. Membranes

The membranes are FILMTEC TW 30-4040 polyamide spiral wound elements [1,4,10,11]. Three membranes were tested - - a new membrane (FTN) and three used ones (FT1, FT2 and FT3) - - which had been producing biosmosed water for hemodialysis for 4y in the second stage

of the RO plant of H6pital Pasteur (Colmar, France) before being changed because of wear problems. This plant has already been described in other papers [1,4,12].

3.2. Pilot

The RO device is constituted of tubes, a pump and a membrane module (Fig. 1). The feed water of the pilot used during the stimulus experiments is ultrapure water pumped out of a tank. The tracer is injected into the pump. The signals are registered by measuring the conductivity in the outlets y,(t) of the membrane ( i - -PT for the permeate and i=R for the rejection side). It also takes into account the dispersion of the tracer in the pump and the pipes. We are interested in the response of the membrane E,(t). yt(t) as it is related to E,(t) in the convolution product:

I

y,( t) -- f du o

(4)

(a) injection device I ~

, + [(membrane by- ~

) , I

membr~me pump module

permeate

conductivity cell

;211-- reject

(b) injection devie~

pump

~_!~asembrane by- ~ pc~ate s - - - -q-dq li Zl---

) ~ conductivity

membrane ~ cell

module reject

Fig. 1. Flow way during stimulus response experiments: (a) for the whole device stimulus response experiments; (b) for apparatus function measurement (membrane by passing).

26 E. Roth et al. / Desalination 129 (2000) 23-33

where g,(t) is the stimulus response of the other elements of the experimental design (i.e., the pump and pipes). The dispersion of the tracer in the pump and the pipes g~(t) in the rejection side (i=R) and in the permeate side (i=PT) is measured by bypassing the membrane (Fig. 1 b). The stimulus response of the membrane E~(t) in the rejection side and the permeate side is obtained by deconvolution of y,(t) by g,(t), respectively, measured in the rejection and the permeate side. The algorithm ofdeconvolution is based on the Kalman filter [13].

3.3. Experimental conditions

Whatever the tested membrane, the permeate flow rate is at Qp=5.00+0.07xl0 5 m3.s 1 by regulation of the feed pressure. The rejection flow rate is set to QR = 1.41~:0.02x10 4 m3.s-~ by turning a valve. The temperature ranged was adjusted to 18.0+0.3 °C.

The three tracing solutions used are: • !.5 M NaCI solution which is generally taken

as a reference salt to study the membrane properties [11 ]

• HC1 solution (1.2 M) • NaCI solution (1.5 M).

Tracer concentrations were followed by measuring every 0.2s the conductivity in the rejection side as well as in the permeate side using a CDM230 conductivy meter and a calibration curve. The surfaces of the membranes were analyzed by ATR infrared with a Brucker IFS 66/S spectrophotometer. Densities of the skin layer of the membranes were measured at 23 °C.

4. Results and discussion

4.1. Stimulus response experiments

4.1.1 Rejection side

The distributions registered in the rejection side are unimodal whatever the studied

0.04

012

0.08

0 0 50 10 20 30 40

time (s)

Fig. 2. Sodium chloride stimulus response experiments E~(t) in the rejection side of the membranes.

membrane and tracer used. These distributions ER(t) are characterized by the mean residence time of the tracer in the feed channel and by the variance, which evaluates the spread (Table 1).

Whatever the tracer, the residence time and the variance of the distributions obtained with the new membrane are smaller. The tracer stays less time in the system and remains gathered; it makes fewer excursions in the membrane [12]. These results confirm those from the feed channel study in a previous work [4].

There is no significant effect of the wear on the mean residence time of NaCI in the membranes (Fig. 2). Nevertheless, the mean residence time (Table 1) of NaOH and HCI in worn-out membranes increases (Figs. 3 and 4). Membranes which show high variances also have poor rejections (Table 1). This phenomenon is empha- sized for HCI tracings: HCI seems to have more excursions into the membrane. It stays longer in the device and is more dispersed. Following the increase of the solute excursions frequency, more solutes cross the membrane and the rejection decreases.

4.1.2 Permeate side For the new membrane, the distributions

obtained in the permeate Epr(t) side are unimodal


Table 1

Mean residence times (±0.1 s) and variances (±2 s z) of the stimulus response experiments recorded in the rejection side and tracer rejection R (±0.1%)

NaOH NaC1 HCI 7 (s) o = (s =) RNaOH (%) t (s) o = (S 2) RNaC, (%) 7 (s) O = (s 2) RHC z (%)

FTN 20.0 10 97.5 20.2 15 99.3 20.2 18 94.8 FT1 21.6 15 92.9 21.6 16 90.4 22.9 28 87.3 FT2 20.0 11 89.1 20.7 17 89.3 21.9 26 78.1 FT3 20.9 14 94.6 20.6 17 98.3 21.1 18 87.5

0"~2

008

ILl

0.04

J 10 20 30 40 50

time (s)

Fig. 3. Sodium hydroxide stimulus response experiments E.(t) in the rejection side of the membranes.

for the stimulus response experiments obtained with NaCI (Fig. 5) and HCI (Fig. 6). For NaOH the stimulus experiments show two maxima (Fig. 7). Transport of solute in a FT 30-4040 RO membrane is mainly done by diffusion [2,8]. The solutes are solvated in the hydrated polyamide membrane and "jump" by replacing one of the hydration water molecules with an electro- attractive polymer group. Also Kotelyanskii et al. [8] found Na + diffuses in the membrane because of exchanges with a polar carbonyl group. C1- involves four water molecules, a carbonyl hydrogen, an amide hydrogen and a phenylene group in its diffusion transport across the membrane.

In the new membrane, the unimodal form of the distribution obtained in the case of tracing

012

008

004

0 0

v

10 20 30 40 50

t ime (s)

Fig. 4. Hydrogen chloride stimulus response experiments ER(t) in the rejection side of the membranes.

with NaCI and HCI solutions results from the "jump" diffusion way of transport across the membrane. The second maximum for the NaOH tracing (Fig. 7) could be explained by the presence of a classical diffusion mode of NaOH in the polymer by "jump" added with acid-base reactions: some OH- could be retarded in their transport by reaction with the labile hydrogen of the rejection skin layer carboxylic groups.

+ OH" ~ ~

o ~ C x O.H o~ .C~ .o .

+ H~O


Table 2

Mean residence times (±0.1 s) and variances (+2 s 2) of the stimulus response experiments recorded in the permeate side and tracer rejection R (i0.1%)

NaOH NaCI HCI t- (S) 0"2 (S 2) RNaOH (%) 7 (S) 0 2 (S 2) RNaCI (%) 7 (S) 0 2 (S 2) RHC I (%)

FTN 29.4 40 97.5 22.5 23 99.3 24.2 52 94.8 FT1 29.3 115 92.9 18.0 80 90.4 19.3 62 87.3

FT2 23.9 131 89.1 10.5 44 89.3 16.9 80 78.1 FT3 29.8 64 94.6 16.9 54 98.3 20.1 45 87.5

o-oIL . . . . . . . . . .

0 10 20 30 40

0.06

0.04

U.l

0.02

1 50 Oz 0 20 40 60

time (s)

Fig. 5. Sodium chloride stimulus response experiments EpT(t ) in the permeate side of the membranes.

time (s) Fig. 6. Hydrogen chloride stimulus response experiments Epr(t ) in the permeate side of the membranes.

0.06 /~ ,

001 _

20 40 60

time (s) Fig. 7. Sodium hydroxide stimulus response experiments E1,r(t ) in the permeate side of the membranes.

For the membranes used, the mean residence times o f the tracers are smaller and the variances are higher than in the new membrane (Table 2). In fact, whatever the tracer, we can observe an early detection o f salt in the permeate: it seems there is a salt leakage as pointed out in a previous work [2]. The solute is transported faster in a worn out membrane.

We can also establish the following relations for the variances, the residence times and the rejections (Table 2):

t,. (NaC1) _< ~,. (HCI) _< ~. (NaOH)


0 2 (NaCl) ~ o 2 (HCI) < 02 (NaOH)

R (HC1) _< R (NaC1) ~- R (NaOH)

Solutes have a particular behaviour in the membrane according to their charge and size: distributions with a low residence time and a small variance signify it will have a good rejection. Also NaC1 is rejected better than HCI. The residence time of NaOH in the membrane cannot be taken into account to establish an affinity order with the membrane because of the acid-base affinity that OH has with the membrane polymer: the distribution is translated into high residence times.

4.2. Determinat ion o f diffusion modes in the membrane

The response of the tracer in the permeate side involves the effect of the transport in the feed channel as well as the transfer of solutes across the membrane and the transport in the permeate channel. We have to interpret the signal globally. The dispersion of the solutes in the different channels is unimodal. The presence of several maxima, each one identified as a permeation mode, is also due to the transfer

across the membrane. The solutes are separated in one to three distributions in accordance with the way they cross the membrane. The best model to represent the permeation of the solute is the dispersed plug flow model characterized by the Peclet number Pe and the tracer space time 1: in the device.

Each stimulus response in the permeate side is modelled by a weighted average of a maximum of four dispersed plug flow distributions, Emod(t):

Emod (/) = E c,'E;(t) (5) i=1,4

with ~ c,= 1. i

The best fitting of the experimental distribution is obtained by minimizing the least square. The identified coefficients Pei, ~ and cj for each four modes (i = 1-4) are given in Tables 3-5.

Whatever the tracer, we can note the presence of three modes whose space time range, respectively, between 19.8 and 24.4 s, 13.0 and 16.5 s, 5.9 and 10.0 s (Tables 3-5). A fourth one, whose space time ranges between 29.4 and 32.3 s, is only present for the NaOH tracings.

The first mode is a remnant of the permeation that occurs in the new membrane. Whatever the

Table 3 Permeation mode characteristics (Peclet number Pe~, space time z~ and weight c~) in the average distribution for NaCI tracing

, FTN FT1 FT2 FT3

e,l "c I 23.4 24.2 22.0 26.7 Pe I 28 21 34 28 c I 0.28 0.36 0.18 0.2 ~z 14.9 16.5 P e 2 27 32 c 2 0.38 0.45 ~3 9.6 8.0 7.2 10.0 Pe 3 18 18 14 26 c 3 0.72 0.26 0.82 0.35

30 E. R o t h et al. / D e s a l i n a t i o n 129 (2000) 2 3 - 3 3

Table 4 Permeation mode characteristics (Peclet number Pe,, space time v, and weight c,) in the average distribution for HCI tracing

FTN FT1 FT2 FT3

% 22.3 24.4 20.9

Pe I 29 21 23 c I 0.74 0.63 0.67 ~2 13.8

Pe 2 47

c2 ~s 9.3 8.0 5.9 Pe s 15 24 l 3 c 3 0.26 0.16 0.33

21.0 24

0.74 13.0 26

Table 5 Permeation mode characteristics (Peclet number Pei, space time zi and weight ci) in the average distribution for NaOH tracing

FTN FT1 FT2 FT3

E/I, zl 19.8 19.6 20.5

Pe I 41 57 75 cj 0.15 0.08 0.19

E2 "~2 13.2

Pe 2 8

c 2 0.21

E3 z3 8.8 9.6

Pe 3 17 20 26 c 3 0.12 0.33 0.35

E¢ z4 30.0 32.3 29.4 32.1 Pe 4 50 33 34 56 c 4 0.73 0.71 0.67 0.81

tracer and the worn-out membrane, it is charac te r ized by lower Pecle t numbers (Tables 3-5) than those characterizing the new membrane permeation mode.

The presence o f space t ime shifted forward modes (modes 2 and 3) indicates the salt leakage. But it does not mean there is a bypass in the membrane because the weights (coefficients c,) o f these modes are different in occurrence with the tracer; interactions between the tracer and the

membrane still occur. The structure o f the polymer has surely evolved in a way o f pore enlargement, but there is no boring through the membrane.

Only in the case o f N aO H stimulus response experiments do we need a fourth mode in the modell ing (Table 5). It models the acid-base affinity which creates a delay in the diffusion o f a part o f the hydroxides in the membrane.


Table 6 Intensities of the absorbance bands

Wave length Intensity (AU) (cm-')

FTN FT1

3312.38 0.065 0.050

FT2 FT3

0.065 0.065

Absorbance bands attribution

H bonding between amid and

2941.16 0.023 0.010 0.010 0.011

1653.19 0.099 0.093 0.098 0.097

1585.91 0.246 0.232 0.209 0.256

1540.84 0.127

1503.84 0.261 0.257 0.227 0.275

1487.94 0.448 0.382 0.334 0.422

1413.16 0.104 0.083 0.089 0.099

1363.64 0.067 0.054 0.051 0.067

1323.95 0.187 0.154 0.149 0.177

1294.57 0.202 0.171 0.167 0.191

1242.35 0.605 0.527 0.473 0.581

1169.34 0.293 0.251 0.224 0.277

1151.10 0.497 0.431 0.379 0.477

ll06.01 0.390 0.327 0.292 0.359

1080.83 0.164 0.128 0.123 0.134

1014.26 0.179 0.155 0.139 0.156

873.60 0.278 0.256 0.233 0.258

853.40 0.267 0.239 0.218 0.239

834.01 0.354 0.320 0.284 0.329

794.60 0.149 0.253 0.125 0.127

715.64 0.265 0.310 0.233 0.248

691.97 0.336 0.195 0.282 0.311

carboxylic group

C-H stretching vibration

Carboxylic group stretching

N-H deformation

Aromatic C=C stretching (varying)

C-N stretching vibration

CO 2 stretching

C-H vibration coupled with the 2941.16 band

Aromatic C-H stretching in plane

Aromatic C-H deformation

vibration

Out of plane

In-plane aromatic ring deformation

Aromatic C-H deformation vibration

Out of plane

Aromatic ring vibration

Aromatic C-H bending out of plane

4.3. M e m b r a n e analyses

To corroborate the structure enlargement o f

the membranes, some physico-chemical analyses

can be envisaged.

The membrane skin layer densities are

measured at 23 °C:

d(FTN) = 0.3 86

d(FT1) = 0.273

d(FT2) = 0.261

d(FT3) = 0.325

It turns out that when the density decreases, the rejection decreases as well (Table 1), and the

structure o f the polymer is enlarged.


Infrared investigations were also made to verify if a surface modification occurred. The spectra of the skin layers of the membranes are twin. Only the intensities of the absorbance bands vary (Table 6). The intensities of the absorbance bands of the IR spectra, the densities of the thin layer of the membranes and the tracer rejection evolve in the same way:

FTN > FT3 > FT1 > FT2

The structure modification of the membrane with the wear out is obvious.

5. Conclusions

Solutes diffusion across a new membrane according to a permeation mode is described by a dispersed plug flow model. With wear, new membrane permeation modes appear. The new membrane permeation still remains with a lower Peclet number.

Also the interpretation of the stimulus response experiments gives information about the changes in the solute transport with the wear out. In fact, the structure enlargement allows the appearance of new diffusion modes across the membrane with low space times.

Physico-chemical analyses confirm the structure modification which allows the appearance of new permeation modes of solutes across the membrane. Consequently, the effi- ciency represented by the rejection decreases.

6. Symbols

Ci

d

- - Weight of the dispersed plug flow distribution the average Ep'(t) in Emod(t)

- - Density, kg.m -3

E~,,~( t ) - -

E m o ~ ( O - -

E R ( t ) - -

g , ( t ) - -

Pe i Qp - -

- -

R T t m

L

y , ( 0 - -

Dispersed plug flow residence time stimulus experiment response distribution Stimulus experiment response distribution in the permeate Average of dispersed plug flow stimulus experiment response distributions Stimulus experiment response distribution in the rejection Experimentally measured apparatus function in the rejection (i=R) and in the permeate ( i = P T ) side Peclet number for mode i Permeate flow rate, m3.s 1 Rejection flow rate, m3.s -1 Membrane rejection, % Temperature, ° C Time, s Mean residence time, s Experimentally measured global stimulus response experiment in the rejection (i=R) and in the permeate ( i = P T ) side

G r e e k

o 2 - - Variance, s 2 zj - - Space time, s

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Desalination, 121 (1999) 183. [6] P.V. Danckwerts, Chem. Eng. Sci., 2 (1953) 1. [7] O. Levenspiel, Chemical Reaction Engineering, 2nd

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[8] F.J. Krambeck, S. Katz and R. Shinnar, Chem. Eng. Sci., 24 (1969) 1497.

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[10] J.M. Dickson, J. Spencer and M.L. Costa, Desalina- tion, 89 (1992) 63.

[11] R.I. Uruma and B.J. Marinas, J. Membr. Sci., 123 (1997) 267.

[12] E. Roth, D6tection et mod61isation du vieillissement

et du colmatage de membranes d'osmose inverse par traitement num6rique de signaux issus de tra~age par des ions. Application ~ l'6tude des membranes FT30-4040 utilis6es dans la pr6paration d'eau ultrapure, Th6se No. 98, MULH 0528, Mulhouse, France, 1998.

[13] R.E. Kalman, SIAM, J. Control, 1 (1961) 152. [14] M.J. Kotelyanskii, N.J. Wagner and M.E. Paulaitis,

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