Reverse osmosis with a cellulose acetate membrane in the reverse orientation

Desalination, 36 (1981) 291-29’7 @ Elsevier Scientific Publishing Company, Amsterdam -

REVERSE OSMOSIS WITH A CELLULOSE IN THE REVERSE ORIENTATION

Printed in The Netherlands

ACETATE

MEMBRANE

J.A.M. SMIT Gorlaeus Labomtories. State University of Leiden. P-0. Box 9502. 2300 RA Leiden (The Nethertands) (Received June 18.1981)

SUMMARY

Salt rejection curves of CA membranes placed with the porous layer towards the infhrent side and the skin towards the effluent side show typical maxima. Analysis of these maxima yields information on the salt permeabilities of the porous layer (ab) and of the skin (w,) in a rather direct way.

SYMBOLS

salt concentration, mol mW3 flow parameters defined by Eq. (4) salt flux mol mS2s-’ J, total voLne flux, m s-l J, - hydrostatic pressure, Pa P r - salt rejection l-I - (=ZZW c,) theoretical osmotic pressure, Pa 0 - reflection coefficient - solute permeability, m SK’ a”- - difference across the skin (i = a) or across the porous layer AZ - difkence across the membrane >

a

-

(i = b)

-Skill

porous layer - normal position of the membrane: skin towards high-pressure side - reverse position of the membrane: porous layer towards the highpressure aide , II influent, effluent 3 * - maximum of the retention curve (reverse position) b

I II

-

J.A_M.

292

SMlT

INTRODUCTION

The use of skinned membranes in reverse osmosis has become common practice. These membranes possess a dense and very selective skin layer supported by a layer of a rather open and porous structure_ The modified celIulose acetate membrane [l] is a well-known example. Due to its asymmetric structure a CA membrane can have two different orientations with respect to the adjacent external solutions. The normal position (in the following to be indicated by I) is the orientation in which the selective skin is turned towards the high-pressure side or the influent side of the salt solution. By reversing the membrane the porous layer appears at the high-pressure side, whereas the skin faces the effluent side (position II). It is on this experimental situation that the attention is focused in this paper. Measurements with a CA membrane in the reverse position provide important additional information on the relevant transport parameters. Using experimental data recently obtained by Jonsson [2] and Henkens [ 31 we are able to reduce our transport equations derived earlier [3] to very simple expressions. As a result the transport properties can be read directly from the retention curves measured with the membrane in the reverse position.

THEORETICAL

Retention curves can be experimentally obtained by measuring the salt retention r and the conjugated volume flux J, at a number of pressure levels, with r defined as

in which ci and ci are the salt concentrations at the influent and effluent sides respectively. In Fig. 1 two retention curves are shown for the normal and the reverse position of the membrane. Clearly the separation of salt and water is strongly influenced by whether the skin faces the high-pressure side or not. By extending a theoretical approach of Jagur-Grodzinski and Kedem [4] we have analysed the difference in separation behaviour for the positions I and II [3] . In this analysis the membrane is thought to consist of two homogeneous elements in series. Following Kedem and Katchalsky [5] we may assign to each separate layer a reflection coefficient ai and a solute permeability coefficient wi in which i (i = a, b) stands for the skin (a) and for the porous layer (b). Here these coefficients are defined as

J, = 0

i=a,b

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1.c

09 r 0.8 <_ -

II

0.6

0.5

OL

03

J 1

,I 0I

3 t

6 I 21

I I

I

I ?

3.16

12 i

1 L

ri

Fig. 1. Retention curves of the cellulose acetate membrane KP 98 in the two orientations: I. Normal orientation with the skin facing the high-pressure side; II. reverse orientation with the skin facing the low-pressure side.

In this equation AiP is the hydrostatic PIXSSUIX difference and Ain the osmotic pressure difference across the membrane element concerned. The pressure differences are chosen in such a way that there is no net displacement of liquid through the membrane. Furthermore Js represents the fiow of neutral salt through the membrane caused by the concentration differences across the membrane elements. Our earlier result using the definitions (2) is easily recapitulated. In the normal position of the membrane the expression for the salt retention reads ‘I = l-

(l-a,) (1-&)(l--a,)+&

(l_Ob) (l-ua,F*)(l--CT*)

% ’

Ob

(3)

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294

in which Fi (i = (I, b) denotes the abbreviation Fi

= exp [-~

~~1

(4)

The salt retention in the reverse position is obtained in a simple way by interchanging the subscripts a and b in Eq. (3) l-

z-1* =

(l--O,) (l--b) t1 -F&j t1 -*a) + F& (1 --oaFa) (1 -f+,)

*a >

(5)

*b

Upon closer inspection of Eq. (3) it appears that rr is a monotonously increasing function of J, in the range of positive values of Ju with an underlimit r + 0 for Ju + 0 and an upper-limit rr -+ oa for Fn + 0 attained at very large vahres of J,. Eq. (5) predicts a different behaviour of the salt retention, rn , which becomes more clear by also considering the derivative

dr,, = (1 -rrr>* w WJ

?(I-,,

+ 56 i

b

-oa

1

(6)

Again in the limit J, --f 0, rII tends to zero and for large values of Ju (Fb + 0) rr1 tends to the reflection coefficient of the layer facing the high-pressure side cb. However, as Eq. (6) shows, rII reaches its maximum at a value of q, which can be calculated from exp

[

1 i:

Jo]

= t1 -*&)*a “,‘ti?a)*a

W&lWa

(7)

The physical explanation of this maximum, already given 131 is based on the phenomenon, that in position II salt can accumulate within the membrane around the interface between the porous layer and the skin. This internal ~oncen~tion polarization increases with increasing values of Jo and counteracts the retention because the internally developed diffusional force drives the salt through the shin. Recent measurements of Jonsson [2] inspired us to transform Eq. (7) into a very operational form. Jonsson succeeded in gathering data for a current type of CA membrane in the reverse position in the range of limiting salt retentions. From his measurements it can be deduced that the values of c$ tend to zero. Moreover it follows from his measurements and our measurements with a comparable type of membrane that the exponent of Eq. (7) may be approximated by two terms of its Taylor series. If we introduce these two simplifications into Eq. (7) we arrive at the surprising result J,* = ‘db

(8)

Thus the parameter w6 may be directly read from tbe retention cme obtained in position II of the membrane! If we substitute Eq. (8) for Eq. (5), again taking the value of ob equal to zero and developing F’ into the first

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two terms of the Taylor series,we find

(9) in which e is the usual base for the natural logarithm. Once the value of o= is known from a measurement in the normal position of the membrane and when it may be used irrespective of the orientation the maximum value r:r allows the calculation of the ratio wb/wa_ In this manner the combination of Eqs. (8) and (9) leads to the determination of the parameters wa and wb.

RESULTS

AND

DISCUSSION

In order to test Eq. (8) and (9) we will make use of the retention curves shown in Fig. 1 and of those measured by Jonsson [2] _ The results have been compiled in Table 1. The CA membranes of the type DDS 995 (Danish Sugar Corporation) were pressurized in the normal position at the maximum pressures indicated [2]. If the membrane is kept sufficiently long under the compaction pressure reasonably stable structures are obtained. The CA membranes KE’ 98 (Eastman Chemical Products) were pressurized in the position of the measurements, i.e. at 70 atm in the normal position and 30 atm in the reverse position. These data are mentioned in the first two coh.unns of Table I_ The limiting retentions measured in the normal position are tabulated as the values of o=_ The values of r,*, and of J,* follow from a simple graphic procedure in which the maximum appearing in the reverse retention curve was localized. The values of w, were calculated from Eq. (9). Jonsson [2] follows a rather complicated procedure to estimate ub from the reteIitioncurve of the reverse position, whereas he calculates the values of w, and o, horn the retention

TABLE

I

PROPERTIES OF CA MEMBRANES CALCULATED FROM RETENTION CURVES NaCL IN WATER OBTAINED IN THE TWO ORIENTATIONS OF THE MEMBRANE

Membrane

DDS 995 KP98

Pressure

aa

G

10 50 100 70130

0.886 0.834 0.824 0.984

0.276 0.132 0.096 0.686

OF

Wa jirn s-’

2.82 (2.87) 1.72 (1.74) 1.20 (1.29) 3.16 -

2.41 3.47 3.69 0.36

(2.39) (3.46) (3.67) (0.29 -

0.54)

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296

curve of the normal position. The values of o, and o+, obtained along this route are mentioned between parentheses. There is fair agreement between the values originating horn the two procedures. The proposed method of determining the relevant parameters has, apart from the advantage of being direct and simple, the advantage of allowing an accurate estimation of wa from the maximum. If the value of oa tends to unity, the estimation of o+ from the retention cUrYe in the normal position can no longer be justified. This calculation requires that (1 - Us) can be measured in a sufficient degree of accuracy. However, the relative error in (1 - a,) amounts oa/( 1 - ~~a)times the relative error in oa. For this reason a rough estimation of wa has been given for the membrane KP 98. The changes in the structure of the membrane DDS 995, induced by the pressure treatment before the measurements, are reflected by the variation found in the values of wa and G+,_ This effect has been discussed [2]. Consequently, the overall reflection coefficient (T defined [6] by the ratio (Ap/All)~,=e will be very sensitive to changes in the membrane structure. For the bilayer-membrane discussed this coefficient is related to the partial quantities according to [4] ci=

Wb o ma + wb =

(10)

A correct experimental determination of o for a bilayer-membrane demands a rather complicated experimental [ 71 or mathematical [ 81 approach. Using the tabulated data we calculate here respectively 0.48, 0.28 and 0.21 for o in the order of increasing compaction of the membrane DDS 995. It seems surprising that o decreases with increasing compaction of the membrane, but this behaviour is in conformity with the changes in the values of wa and ub. It is also confirmed experimentally by Pusch 191, who reports values of o in a quite analogous system being approximately 0.5 for an untreated and 0.3 for a pressurized CA membrane. Also Eq. (10) shows favourable perspectives for application. In combination with Eq. (9) it yields

-=eG

( >

u (11) % As 0 can be estimated from osmotic experiments [7,8], again ma and wb can be evaluated from the maximum of the retention curve in the reverse position. 1 -r;

1+%

CONCLUSIONS

The retention curve of an asymmetric CA membrane in the reverse orientation has a maximum at a position where the volume flow equals the solute permeability of the porous layer (dotted line in Fig. 1). The height of the

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maximum allows the estimation of the solute permeability of the skin if the reflection coefficient of the skin or the overall reflection coefficient of the membrane is available from a supplementary measurement (Eq. 9 or Eq. 11) Along the above lines a method can be followed leading to a rapid determination of the characteristic psrameters. Agreement is found between the results from the proposed method and those obtained from .a more complicated method using the full range of the curve developed by Jonsson [Z] (Table I).

ACKNOWLEDGEMENT

The author thanks Dr. J. van Daalen (Leiden, The Netherlands) for critically reading the manuscript.

REFERENCES 1. 2. 3. 4. 5. 6. 7.

8. 9.

S. Loeb and S. Sourirajan, Sea Water Demineraliaation by an Osmotic Membrane, Advanc. Chem. Ser., 38 (1963) 117. G. Jonsson, The Influence of the Porous Sublayer on the Salt Rejection and Reflection Coefficient of Asymmetric CA Membranes, Desalination, 34 (1980) 141. W.C.M. Henkens and J.A.M Smit. Salt Rejection and Flux in Reverse Osmosis with Compactible Membranes, Desalination, 28 (1979) 65. J. Jagur-Grodzinski and 0. Kedem, Transport Coefficients and Salt Rejection in Uncharged Hyperfiltration Membranes, Desalination, I (1966) 327. 0. Kedem and A. Katchalsky, Permeability of Composite Membranes, Trans. Farad. Sot., 59 (1963) 1941. A.J. Staverman. The Theory of Measurements of Osmotic Pressure, Rec. Trav. Chim. Pays Bas, 70 (1951) 344. W.C.M. Henkens, J.C. Eijserrnans and J-AM. Smit, Osmotic Properties of a Modified Cellulose Acetate Membrane: The Reflection Coefficient and its Dependence on the Volume Flow History, J. Membr. Sci., 5 (1979) 149. C.W. Versluijs, Transient Osmotic Pressures Across Composite Membranes, Thesis, Leiden, 1981. W. Pusch, Transport Coefficients of Asymmetric Cellulose Acetate Membranes, Desalination, 16 (1975) 65.