DESALINATION

E L S E V I E R Desalination 127 (2000) 69-77 w ww.elsevier.com/locate/desal

Modelling of stimulus response experiments in the feed channel of spiral-wound reverse osmosis membranes

E. Roth a, B. Fabre a*, A. Accary a, G. Thomas b aUniversitO de Haute Alsace, Laboratoire Gestion des Risques et Environnement,

25 rue de Chemnitz, F-68200 Mulhouse, France Tel. +33 (3) 89 32 76 73; Fax +33 (3) 89 32 76 61; email: B.Fabre@univ-mulhouse.fr

bCPE, Laboratoire d'Automatique et Gdnie des ProcddOs, 43 Bd D u l l Novembre 1918, F-69622 Villeurbanne, France

Received 21 April 1999; accepted 30 July 1999

Abstract

Reverse osmosis is commonly used to produce ultrapure water which is necessary in hemodialysis to prepare the dialyzing liquid. We have managed to test some spiral-wound FT30-4040 membranes by analyzing their response to a stimulus injection of tracer. The shape of the distribution of the tracer in the rejection side is compared for different membranes, a new and two used ones, and different tracers in order to study the evolution of the interactions between the solutes and the membrane with wear. We used three tracing solutions: sodium chloride solution (1.5M), hydrochloric acid (1.2 M) and sodium hydroxide (1.5 M) to reach acid or basic pH. The distributions of tracer detected in the rejection side are unimodal with a tail which is greater in the case of the hydrochloric tracing. These results enable us to establish an increasing affinity for NaOH, NaCI and HCI with the membrane. We represent the feed channel between the sheet of membranes by a series of perfect mixing cells with exchange. The modelling of the space between the membrane sheets by a series of perfect mixing cells with exchange, the dead zone representing the membrane, gives good results. It gives prominence to the existence of excursions of the solute in the membrane.

Keywords: Reverse osmosis; Tracing; Stimulus response experiments; Kalman filter; Modelling

1. I n t roduc t i on The rejection properties o f the membrane play a key role in the success o f the process. Usually the

Reverse osmosis (RO) is commonly used to produce ultrapure water which is necessary in performances of membranes are exposed in terms hemodialysis to prepare the dialyzing liquid [1]. of rejection or pure water permeability [2]. We

have managed to test some spiral-wound FT30- 4040 membranes by analyzing their response to

*Corresponding author, a stimulus injection o f tracer. The distribution of

0011-9164/00/$- See front matter © 2000 Elsevier Science B.V. All rights reserved Pll: SO011-9164( 99)00193 -9

70 F~ Roth et al. / Desalination 127 (2000) 69-77

the tracer in the rejection side is compared for residence time T of salt in the system and its different membranes, a new and two used ones, variance o 2, which represents the square of the and different tracers, spread of the distribution. For continuous (resp.

The first section of this paper deals with the discrete measurements) they are defined as [9]: theory of residence time distribution in a system. This notion is enlarged to the concept of contact time distribution when the tracer reacts with the -t= f t.E(t).dt (resp. -t= ~ t i.Et,.At) (1) studied system. It also emphasizes the necessity 0 of using a deconvolution algorithm to separate the membrane response to stimulus from the whole system response. This algorithm is based f f 2 = f (t--t)2"E(t)'dt on the Kalman filter [3,4]. In the second section 0 (2)

[r 2 ] we describe the experimental design and esp. (I2= E t, "Et'At-(-t) 2 conditions as well as the measurement procedures. The results are presented in the third section together with a discussion. The last where the (t,] are the equispaced measurement section presents a modelling of the feed channel times and A~ j~l the measurement step. in a series of mixing cells with exchange.

2.2. Modelling stimulus experiments response 2. Theory curves

2.1. Residence time distributions (RTD) A simple fitting of the distribution with a

Tracing is a commonplace technique to study mathematical function does not give any infor- the hydrodynamic of a system. Making sure the mation on the studied system. The model is tracer really represents the hydrodynamic of the suggested by the physics and the design of the system, the tracing is based on the concept of reactor. The global flow results from placing the residence time distribution. This technique, different zones side by side in which there are which is described elsewhere [4,5], emphasizes special flow conditions. We can single out five the existence of the studied system's dysfunction special flows [6]: such as dead volumes, by-pass and recycling, 1. the ideal plug flow reactor: the elements of which can then be tracked by simple observation flow evolve independently. The signal is un- of its shape [6]. changed in the outlet of the system;

When a tracer reacts with the studied system, 2. the perfect mixing cell (Fig. 1): in such a we reach the concept of contact time distribution zone the concentration is made uniform by (CTD) [7,8]. For isolating the CTD of the tracer intensive mixing; in the membrane, we need to find a real tracer 3. the by-pass; which does not react with the membrane [7,8]. 4. the series of J perfect mixing cells: this This is not the subject of this paper. The device is equivalent to a plug flow with comparison of the shape of the distributions of dispersion. The stimulus response of such a tracer reacting with the membrane is sufficient to device is distinguish between a new and a worn out one.

We will characterize the distributions E(t~)dts E(t) = ( J ) . tJ-" exp (-J" t/z) recorded in the rejection side by the mean (J-l)! (3)

E. Roth et al. / Desalination 127 (2000) 69-77 71

(2 Q vl

lrZR ocQ ocQ

Fig. 1. Perfect mixing cell. V ?

Fig. 2. Perfect mixing cell with exchange. where t is the space time in the series;

5. the series of perfect mixing cells with exchange (Fig. 2): they include a dead zone in which the tracer makes excursions. The device is 2.3. DeconvoIution with the Kalmanfilter

characterized by The tracer is injected upstream of the pump • a mixing time (Fig. 3a). The distribution recorded in the outlet

y(t) takes into account the dispersion of the tracer t m - V2 (4) in the pump and the pipes. We are interested by

ec.Q the response of the membrane x(t). From a mathematical point of view y(t) is related to x(t) in the convolution product:

where c¢ is the fraction of flow entering the dead zone.

• the rate between the two perfect mixed y ( t ) = ( x ( u ) . g ( t - u ) . d u , forallt>_0 (7) volume and the dead volume d

0

K - V2 (5) where g(t) is the stimulus response of the other V~ elements of the experimental design (i.e., the

pump and the pipes). The dispersion of the tracer

The series is characterized by a space time in the pump and the pipes g(t) is measured by by- constant: passing the membrane (Fig. 3b). The stimulus

response of the membrane x(t) is obtained by deconvolution of y(t) by g(t). The algorithm of

J" V 1 - (6) deconvolution is based on the Kalman filter Q whose theory is described elsewhere [3].

72 E. Roth et aL / Desalination 127 (2000) 69-77

injecti°n device 7 ~----I "

(a) ~( membrane by- , permeate _ j - - - - > - - l . ~ ~s ¢, ~ . ~ : ,

• • " i : . . . . :

/ ~ " / cellc°nductivit¢~ .... ....

• h. ~ '" ~ ' ~ ~ ~ l l l l l ~ " " ..... membrane C pump module - - ' ........

reject i ecti°n (b) aevic "~ "~ } mLe braneby permeate

.

~ ) , . ~ conductN~ty " " • .- l - " c e l l .

membr'ane ~ ' C ! - - , ~ pump ........ module - "

reject Fig. 3. Flow way during stimulus response experiments: (a) for the whole device stimulus response experiments; (b) for apparatus function measurement (membrane by passing).

3. Experimental detect the tracer (Fig. 3). Two sets of experiments 3.1. Membranes are carried out. In the first one stimulus

experiments measure the whole response of the We studied polyamide spiral-wound mem- device. Fig. 3a shows in bold the flow during

brane elements FILMTEC TW 30-4040 [4,9-11 ]. these experiments. In the second set of experi- Three membranes were tested: a new one (FTN) ments the dispersion in the pump and the pipes is and two used ones (FT1 and FT2), which had measured by by-passing the membrane (Fig. 3b). been producing biosmosed water for hemo- The feed water of the pilot used during the dialysis for 4 y in the second stage of the RO stimulus experiments is ultrapure water pumped plant of <<H6pital Pasteur>> (Colmar, France) out of atank. before being changed because of wear problems. The plant has already been described in other papers [4,9,12]. 3.3. RTD experimental conditions

We worked at a sufficiently low pressure (4.0x 105 Pa) to avoid permeation. The feed and

3.2. Pilot the rejection flow rate of has been set at Q= The pilot contains a pump, a module for the 1.41 × 10 -4 m 3 s - I. Temperature ranged between

membrane and an on-line conductivity cell to 18.0 + 0.3°C.

E. Roth et al. /Desalination 127 (2000) 69-77 73

3.4. Tracing solutions V _ 17.7±0.2 s " ~ m b r -

Three tracing solutions were used: Q • a 1.5M sodium chloride solution which is

The global space time in the device is also z= generally taken as a reference salt to study the membrane properties [ 11 ]; "l~mbr + 2 "tea v : 19.4 + 0.2 s.

The distributions of tracer detected in the • two other solutions, each one containing one rejection side (Figs. 5-7) are unimodal with a tail

ion belonging to the ionization product of which is greater in the case of hydrochloric water: a hydrochloric acid solution (1.2M) tracing. In a previous work, Van Gauwbergen and and a sodium hydroxide solution (1.5M) to

Baeyens [14] found similar results by tracing a reach acid or basic pH. Millipore RO 15 spiral-wound RO module with a

calcium chloride solution at atmospheric pressure 3.5. Detection andacquis i t ion and flow rate ranging between 2.8 and 9.5×

10-5 m3.s I. Tracer concentrations in the rejection side

The shape of the distribution depends on the were determined using a CDM230 conductivity

tracer: the membrane is not inert to it. The tracer meter and a calibration curve. Data were

makes excursions into the membrane. Table 1 collected by means of a TURBO PASCAL acquisition program connected to the conduct- gives the mean residence time and the variance of

each distribution. The mean residence times and ivity meter. The acquisition frequency was 5 Hz and At=0.2s. the variances evolve similarly whatever the

membrane:

4. Results and discussion z ~ t (NaOH)_< t (NaCI)_< t (HCI) (8)

In order to analyze the mean residence time of o 2 (NaOH) _< o 2 (NaC1) 02 (HCI) the tracer in the device, it is useful to calculate the theoretical space time of the flow in the module. For this purpose, we need to know the These results allow us to establish an exact dimensions of the membrane module. Each increasing affinity for NaOH, NaCI and HCI for sheet of the membrane has an area of 1.35 ×0.89 = the membrane. NaOH is most efficiently rejected 1.20+0.02m 2. The spacer thickness is 0.77× electrolyte by the membrane, it stays more 10-3m. Knowing its porosity (~=0.89 [13]), the clustered than NaCI and HC1 within the feed

channel. OH- spends less time in the membrane space between the three sheets of membrane can be calculated as 2.50+0.05×10-3m 3. There are than CI- and H3 O+ much more than Na ÷. H3 O+ two cavities on either side of the membrane has a particular affinity with the membrane due sheets whose volumes are 1.20±0.02 10-4m3.The to its small size. The presence of tails in the space time Zca v of the flow in these cavities is also distributions does not at all mean that there are

some dead volumes in the spiral-wound module, V as suggested by Van Gauwbergen and Baeyens

= c a v = 0.85±0.05 s [14]. In fact, the mean residence time of the cav Q tracer in the membrane device is greater than the

theoretical space time. In classical tracing and the space time z of the flow between the experiments data treatment, this means that there membrane sheets is is a by-pass in the module but stimulus response

74 E. Roth et al. / Desalination 127 (2000) 69-77

Table 1 Residence time and variance of the distribution recorded for each tracer and each membrane

NaOH NaCl HCI

L (S) 02 ($2) t-s (S) O2 ($2) ts (S) 02 (S 2)

FTN 22.7 39 22.9 55 24.8 60 FT1 24.3 39 24.5 65 25.3 91 FT2 23.5 31 23.2 50 24.2 56

experiment curves are not characteristic of such absorbance intensity (Table 2) with wear out a phenomenon. Tails are different for each tracer, could mean the structure is enlarged and that is which means the contact distribution between the why it is less efficient in removing solutes as tracer and the membrane is different for each demonstrated in stimulus response experiments. tracing solute. The membrane seems to play the No further information was given by these ATR role of a dead volume, analyses. A measurement of the density of the

The worn-out membranes react differently skin layer of the membranes at 23 °C confirms than the new one. The mean residence time of the that the density of a worn-out membrane tracer in the new membrane is less than that in rejection layer (dFT~ =0.273, dFT 2 = 0.325)is lower the used ones (Table 1). The tracer spends a than the new membrane (dvry=0.386); the longer time in the worn-out membranes: it makes reticulation state is lower. more excursions into the membrane. Conse- Modelling - - By analyzing tracer-response quently, the spread of the curves, represented by curves in hollow-fibre RO modules, Gill et al. the variance (Table 1), increases in the worn-out [15] found the plug flow model best represents membranes. The rejection of the solute far from the flow pattern rather than a complete mixed the membrane surface decreases. The structure of model. We choose to distinguish the area the membrane has evolved with use. It seems to between the sheets of membranes from the be less dense to allow solute excursions, membranes where excursions of tracer can occur.

In order to study the membrane structure We also represent the feed channel between the modifications, some ATR infrared spectra of the sheet of membranes by a series of perfect mixing polyamide rejection side of the new membrane cells with exchange (Fig. 4). The simulation is FTN and the worn out ones have been made. made using the software DTS 3.1 developed by Table 2 gives the position of the new membrane Progepi. Two perfect mixing cells representing absorbance bands in cm- ~, the intensities of these the cavities on both sides of the membrane sheets bands for the three membranes and the are included in the model. The space times in the absorbance attributions. The spectra of FT1 and series of mixing cells with exchange and in both FT2 are quite similar. Spectra are characteristic of the cavities are set at their estimated values ofpolyaromatic polyamide (Table 2). The worn- found in the previous section. In the simulation out membrane spectra and the new membrane the number J of cells in the series, the mixing one are twins. The only difference lies in the time t m between a perfect mixed cell and the absorbance band intensity which is a little higher exchange zone, the dead volume V,, and the rate for the new membrane. The diminution of the between the perfect mixed volume and the dead

E. Roth et al . / Desalination 127 (2000) 69-77 75

Table 2 ATR infrared spectra of the polyamide rejection side

Wave length Intensity (AU) Intensity (AU) Intensity (AU) Absorbance bands attribution (cm- 1 ) FTN FT5 FT7

3312.38 0.065 0.050 0.065 H bonding between amid and carboxylic group 2941.16 0.023 0.010 0.011 C-H stretching vibration 1653.19 0.099 0.093 0.097 carboxylic group stretching 1585.91 0.246 0.232 0.256 N-H deformation 1540.84 0.127 Aromatic C=C stretching (varying) 1503.84 0.261 0.257 0.275 C-N stretching vibration 1487.94 0.448 0.382 0.422 1413.16 0.104 0.083 0.099 CO2- stretching 1363.64 0.067 0.054 0.067 C-H vibration coupled with the 1323.95 0.187 0.154 0.177 2941.16 band 1294.57 0.202 0.17 l 0.191 Aromatic C-H stretching in plane 1242.35 0.605 0.527 0.581 1169.34 0.293 0.25 l 0.277 Aromatic C-H deformation vibration 1151.10 0.497 0.431 0.477 out of plant 1106.01 0.390 0.327 0.359 1080.83 0.164 0.128 0.134 1014.26 0.179 0.155 0.156 In plane aromatic ring deformation 873.60 0.278 0.256 0.258 Aromatic C-H deformation vibration 853.40 0.267 0.239 0.239 out of plane 834.01 0.354 0.320 0.329 794.60 0.149 0.253 0.127 Aromatic ring vibration 715.64 0.265 0.310 0.248 691.97 0.336 0.195 0.311 Aromatic C-H bending out of plane

Table 3

Output of the model

NaCI HCI NaOH

J t,, (s) V m (m 3) J t m (s) V,, (m 3) J t m (s) V m (m 3)

FTN 41.8 3.0 4.3×10 -4 57.2 3.2 6.8xl0 -4 50.3 2.2 3.5x10 -4 FTI 41.9 2.5 6.1x10 -4 54.8 2.1 6.4×10 -4 52.0 1.8 6.0x10 -4 FT2 34.5 2.5 5.0×10 4 45.8 2.4 5.7×10 -4 47.8 1.7 5.2x10 -4

volume K are identified at the least square, the simulation. Experiments are represented with

Table 3 gives J, Vm and tm. triangles, squares and asterisks, respectively, for

Figs. 5 -7 show in a simple line the results of NaOH, NaCl and HCI tracers.

76 E Roth et al. / Desalination 127 (2000) 69-77

. . . . . . . . . . . . . . . . . s e r i e s o f . / p e r f e c t OlOO . . . . . .

mixing ceils with ,, NaOH exchange NaCI

o,o, J Q

....... • .... I ertect mixing cells 0050

i~] representing the mixing volumes on each side of the oo25 membrane sheets

Fig. 4. Model for the membrane device, o , 0 20 40 60

t ime (s~

F ig . 5. S t i m u l u s r e s p o n s e e x p e r i m e n t s d i s t r i b u t i o n s for Whatever the membrane, the model for the the FTN membrane.

HCI tracing needs (1) the greatest number o f mixing cells and (2) the greatest dead volume.

HCI seems to make many more excursions in the o.10o . . . . . . . . . . membrane material; it has the greatest affinity Nac~ with the polymer. Modelling the tracing with i He, N aOH needs low mixing times t,, and dead o075 NaOH

volumes Vm, whatever the tracer. The tracer goes "~ quickly and deeper into the worn-out membranes. 0.050

0.025

5. Conclusions j O , j , , , - 1 -

T h e study o f the stimulus response 20 40 60

experiments reveals the difference o f behaviour time (s)

o f a membrane according to a particular solute. Fig. 6. Stimulus response experiments distributions for

Regarding the distribution moments , we can theFT1 membrane.

establish an order o f affinity for the different solutes and the membrane, new ones or worn

+ ones. H3O makes more excursions than Na + into 0,oo

v NaOH the membrane and CI- more than OH-. The worn- HC,

NaCI out membrane distributions are characterized by o ors greater residence t ime and variance values than =

the new membrane, whatever the tracer. That ~ 0.050

clearly means that solutes make more excursions

into worn-out membranes. Worn-out membranes 0.o25

J seem to have lost their rejection capacity. Their structure might be enlarged (lower absorbance band intensities and density), o , - . , 20 40 60

The model l ing o f the space between the time(s)

membrane sheets by a series o f perfect mixing Fig. 7. Stimulus response experiments distributions for cells with exchange, the dead zone representing the FT2 membrane.

E. Roth et al. / Desalination 127 (2000) 69-77 77

the membrane , gives good results. It conf i rms the Re fe r ences

existence o f excursions o f the solute within the m e m b r a n e according to a structure modif icat ion [1] R.A Laurence and S.T. Lapierre, Amer. J. Kidney

o f the rejection layer with use. Dis., 25(5) (1995) 738. [2] S. Kimura, Desalination, 100 (1995) 77. [3] R.E. Kalman, J. Control, 1 (1961) 152.

6. S y m b o l s [4] E. Roth, M. Kessler, B. Fabre and A. Accary, Desalination, 121 (1999) 183.

d - - density, g .cm -3 [5] P.V. Danckwerts, Chem. Eng. Sci., 2(1) (1953) 1. E(t) - - exit age distribution (RTD) [6] O. Levenspiel, Chemical Reaction Engineering, 2nd g(t) - - st imulus response o f the apparatus ed., Wiley, New York, 1972. J - - number o f cell [7] F.J. Krambeck, S. Katz and R. Shinnar, Chem. Eng. Q - - f low rate, m3.s q sci., 24 (1969) 1497. T - - temperature, °C [8] R. Shinnar, P. Naor and S. Katz, Chem. Eng. Sci., 27

t - - t ime, s (1972) 1627. t- - - mean residence t ime, s [9] E. Roth, 13. Fabre, A. Accary and B. Failer, Rev. Sci.

t m - - mix ing t ime in the dead volume, s Eau, 3 (1998) 409. V 1 - - vo lume o f the perfect mixing cell, m 3 [10] J.M. Dickson, J. Spencer and M.L. Costa, Desalina- V 2 - - dead volume, m 3 tion, 89 (1992) 63. I'm - - dead volume, m 3 [11] R.I. Uruma and B.J. Marinas, J. Membr. Sci., 123

x(t) - - membrane RTD (1997) 267. y(t) - - normed outlet detected signal [12] E. Roth, D6tection et moddisation du vieiUissement

et du colmatage de membranes d'osmose inverse par traitement num6rique de signaux issus de tra~age par

G r e e k des ions. Application ~ l'6tude des membranes FT30- 4040 utilis6es dans la pr6paration d'eau ultrapure,

- - propor t ion o f f low rate going in the Th~se N ° 98, MULH 0528, Mulhouse, France, 1998. dead vo lume [13] G. Schock and A. Miquel, Desalination, 64 (1987)

0 2 - - variance, s 2 339.

At - - measu remen t step, s [14] D. Van Gauwbergen and J. Baeyens, Desalination, 1: - - space t ime, s 110 (1997) 287. Zcav - - space t ime in the cavities, s [15] W.N.Gill, M.R.Matsumoto, A.L. Gill and Y.-T. Lee,

" ~ m b r - - space t ime in the membrane sheets, s Desalination, 68 (1988) 11.